vector combination vs time

7 Fév 2021
3 Réponses
Mise à jour 10 Fév 2021
11 Vues (30 jours)

0 votes

Hello everybody..
I have troubles in combinating some vectors respect to time.
I have some data recorded from previous experiments into vectors containing measuring time, body displacement (x), force acting upon a body etc.
Now I need to express the force vector respect time ( that should match with the time measured during the esperiment) but I am not able to do that neither in matlab nor simulink.
For example another problem that I have is that I'd like to calculate the body velocity by deriving the space respect to time. I tried but as 'x' is only a vector and not a function, matlab promps an error.
How can I match the vectors respect to my time vector. I know it is a stupid question, but I am not able to get on top of it.
Every help and advice would be very appreciated.
Best regards
Gabriele

Connectez-vous pour répondre à cette question.

Réponses (3)

Walter Roberson
Walter Roberson le 7 Fév 2021

1 vote

Instead of using
velocity = diff(space) ./ diff(time);
Use
velocity = gradient(space, time);

4 commentaires
Afficher 2 commentaires plus anciens Masquer 2 commentaires plus anciens

Gerardo Gabriele
Gerardo Gabriele le 7 Fév 2021
thank you very much! And for expressing the force respect to time ( so obtaining F(t)) do you have any idea? Thanks again
Walter Roberson
Walter Roberson le 7 Fév 2021
You indicated you already have input for force operating on the body, so it is not clear what you would be calculating?
Perhaps you are looking for
acceleration = gradient(velocity, time);
Force = acceleration .* mass;
This assumes that mass is either constant or a vector the same length as time.
Gerardo Gabriele
Gerardo Gabriele le 8 Fév 2021
with the acceleration i have this graphic as result.
Shouldn't it be just a line?
Walter Roberson
Walter Roberson le 8 Fév 2021
Ran in:
Ran in:
load handel
space = y(1:500,1);
time = (0:size(space,1)-1)/Fs;
velocity = gradient(space, time);
acceleration = gradient(velocity, time);
subplot(3,1,1); plot(time, space); ylabel('position');
subplot(3,1,2); plot(time, velocity); ylabel('velocity');
subplot(3,1,3); plot(time, acceleration); ylabel('acceleration');

Connectez-vous pour commenter.

Giulio Rossi
Giulio Rossi le 10 Fév 2021

0 votes

I have those 2 vectors posted below, with values recorded from experimental measurements. when I do the gradient (vp,t) it keeps on giving me the aforementioned plot, with all these kind of "spikes". How can i solve the problem?
Another question...How can I integrate the velocity respect to time using the 2 vectors? matlab promps an error telling Vp is not a function but an array.
Thanks everyone for your kind help.
t=[0.000
0.001
0.002
0.002
0.003
0.004
0.005
0.006
0.006
0.007
0.008
0.009
0.010
0.010
0.011
0.012
0.013
0.014
0.014
0.015
0.016
0.017
0.018
0.018
0.019
0.020
0.021
0.022
0.022
0.023
0.024
0.025
0.026
0.026
0.027
0.028
0.029
0.030
0.030
0.031
0.032
0.033
0.034
0.034
0.035
0.036
0.037
0.038
0.038
0.039
0.040
0.041
0.042
0.042
0.043
0.044
0.045
0.046
0.046
0.047
0.048
0.049
0.050
0.050
0.051
0.052
0.053
0.054
0.054
0.055
0.056
0.057
0.058
0.058
0.059
0.060
0.061
0.062
0.062
0.063
0.064
0.065
0.066
0.066
0.067
0.068
0.069
0.070
0.070
0.071
0.072
0.073
0.074
0.074
0.075
0.076
0.077
0.078
0.078
0.079
0.080
0.081
0.082
0.082
0.083
0.084
0.085
0.086
0.086
0.087
0.088
0.089
0.090
0.090
0.091
0.092
0.093
0.094
0.094
0.095
0.096
0.097
0.098
0.098
0.099
0.100
0.101
0.102
0.102
0.103
0.104
0.105
0.106
0.106
0.107
0.108
0.109
0.110
0.110
0.111
0.112
0.113
0.114
0.114
0.115
0.116
0.117
0.118
0.118
0.119
0.120
0.121
0.122
0.122
0.123
0.124
0.125
0.126
0.126
0.127
0.128
0.129
0.130
0.130
0.131
0.132
0.133
0.134
0.134
0.135
0.136
0.137
0.138
0.138
0.139
0.140
0.141
0.142
0.142
0.143
0.144
0.145
0.146
0.146
0.147
0.148
0.149
0.150
0.150
0.151
0.152
0.153
0.154
0.154
0.155
0.156
0.157
0.158
0.158
0.159
0.160
0.161
0.162
0.162
0.163
0.164
0.165
0.166
0.166
0.167
0.168
0.169
0.170
0.170
0.171
0.172
0.173
0.174
0.174
0.175
0.176
0.177
0.178
0.178
0.179
0.180
0.181
0.182
0.182
0.183
0.184
0.185
0.186
0.186
0.187
0.188
0.189
0.190
0.190
0.191
0.192
0.193
0.194
0.194
0.195
0.196
0.197
0.198
0.198
0.199
0.200
0.201
0.202
0.202
0.203
0.204
0.205
0.206
0.206
0.207
0.208
0.209
0.210
0.210
0.211
0.212
0.213
0.214
0.214
0.215
0.216
0.217
0.218
0.218
0.219
0.220
0.221
0.222
0.222
0.223
0.224
0.225
0.226
0.226
0.227
0.228
0.229
0.230
0.230
0.231
0.232
0.233
0.234
0.234
0.235
0.236
0.237
0.238
0.238
0.239
0.240
0.241
0.242
0.242
0.243
0.244
0.245
0.246
0.246
0.247
0.248
0.249
0.250
0.250
0.251
0.252
0.253
0.254
0.254
0.255
0.256
0.257
0.258
0.258
0.259
0.260
0.261
0.262
0.262
0.263
0.264
0.265
0.266
0.266
0.267
0.268
0.269
0.270
0.270
0.271
0.272
0.273
0.274
0.274
0.275
0.276
0.277
0.278
0.278
0.279
0.280
0.281
0.282
0.282
0.283
0.284
0.285
0.286
0.286
0.287
0.288
0.289
0.290
0.290
0.291
0.292
0.293
0.294
0.294
0.295
0.296
0.297
0.298
0.298
0.299
0.300
0.301
0.302
0.302
0.303
0.304
0.305
0.306
0.306
0.307
0.308
0.309
0.310
0.310
0.311
0.312
0.313
0.314
0.314
0.315
0.316
0.317
0.318
0.318
0.319
0.320
0.321
0.322
0.322
0.323
0.324
0.325
0.326
0.326
0.327
0.328
0.329
0.330
0.330
0.331
0.332
0.333
0.334
0.334
0.335
0.336
0.337
0.338
0.338
0.339
0.340
0.341
0.342
0.342
0.343
0.344
0.345
0.346
0.346
0.347
0.348
0.349
0.350
0.350
0.351
0.352
0.353
0.354
0.354
0.355
0.356
0.357
0.358
0.358
0.359
0.360
0.361
0.362
0.362
0.363
0.364
0.365
0.366
0.366
0.367
0.368
0.369
0.370
0.370
0.371
0.372
0.373
0.374
0.374
0.375
0.376
0.377
0.378
0.378
0.379
0.380
0.381
0.382
0.382
0.383
0.384
0.385
0.386
0.386
0.387
0.388
0.389
0.390
0.390
0.391
0.392
0.393
0.394
0.394
0.395
0.396
0.397
0.398
0.398
0.399
0.400
0.401
0.402
0.402
0.403
0.404
0.405
0.406
0.406
0.407
0.408
0.409
0.410
0.410
0.411
0.412
0.413
0.414
0.414
0.415
0.416
0.417
0.418
0.418
0.419
0.420
0.421
0.422
0.422
0.423
0.424
0.425
0.426
0.426
0.427
0.428
0.429
0.430
0.430
0.431
0.432
0.433
0.434
0.434
0.435
0.436
0.437
0.438
0.438
0.439
0.440
0.441
0.442
0.442
0.443
0.444
0.445
0.446
0.446
0.447
0.448
0.449
0.450
0.450
0.451
0.452
0.453
0.454
0.454
0.455
0.456
0.457
0.458
0.458
0.459
0.460
0.461
0.462
0.462
0.463
0.464
0.465
0.466
0.466
0.467
0.468
0.469
0.470
0.470
0.471
0.472
0.473
0.474
0.474
0.475
0.476
0.477
0.478
0.478
0.479
0.480
0.481
0.482
0.482
0.483
0.484
0.485
0.486
0.486
0.487
0.488
0.489
0.490
0.490
0.491
0.492
0.493
0.494
0.494
0.495
0.496
0.497
0.498
0.498
0.499
0.500
0.501
0.502
0.502
0.503
0.504
0.505
0.506
0.506
0.507
0.508
0.509
0.510
0.510
0.511
0.512
0.513
0.514
0.514
0.515
0.516
0.517
0.518
0.518
0.519
0.520
0.521
0.522
0.522
0.523
0.524
0.525
0.526
0.526
0.527
0.528
0.529
0.530
0.530
0.531
0.532
0.533
0.534
0.534
0.535
0.536
0.537
0.538
0.538
0.539
0.540
0.541
0.542
0.542
0.543
0.544
0.545
0.546
0.546
0.547
0.548
0.549
0.550
0.550
0.551
0.552
0.553
0.554
0.554
0.555
0.556
0.557
0.558
0.558
0.559
0.560
0.561
0.562
0.562
0.563
0.564
0.565
0.566
0.566
0.567
0.568
0.569
0.570
0.570
0.571
0.572
0.573
0.574
0.574
0.575
0.576
0.577
0.578
0.578
0.579
0.580
0.581
0.582
0.582
0.583
0.584
0.585
0.586
0.586
0.587
0.588
0.589
0.590
0.590
0.591
0.592
0.593
0.594
0.594
0.595
0.596
0.597
0.598
0.598
0.599
0.600
0.601
0.602
0.602
0.603
0.604
0.605
0.606
0.606
0.607
0.608
0.609
0.610
0.610
0.611
0.612
0.613
0.614
0.614
0.615
0.616
0.617
0.618
0.618
0.619
0.620
0.621
0.622
0.622
0.623
0.624
0.625
0.626
0.626
0.627
0.628
0.629
0.630
0.630
0.631
0.632
0.633
0.634
0.634
0.635
0.636
0.637
0.638
0.638
0.639
0.640
0.641
0.642
0.642
0.643
0.644
0.645
0.646
0.646
0.647
0.648
0.649
0.650
0.650
0.651
0.652
0.653
0.654
0.654
0.655
0.656
0.657
0.658
0.658
0.659
0.660
0.661
0.662
0.662
0.663
0.664
0.665
0.666
0.666
0.667
0.668
0.669
0.670
0.670
0.671
0.672
0.673
0.674
0.674
0.675
0.676
0.677
0.678
0.678
0.679
0.680
0.681
0.682
0.682
0.683
0.684
0.685
0.686
0.686
0.687
0.688
0.689
0.690
0.690
0.691
0.692
0.693
0.694
0.694
0.695
0.696
0.697
0.698
0.698
0.699
0.700
0.701
0.702
0.702
0.703
0.704
0.705
0.706
0.706
0.707
0.708
0.709
0.710
0.710
0.711
0.712
0.713
0.714
0.714
0.715
0.716
0.717
0.718
0.718
0.719
0.720
0.721
0.722
0.722
0.723
0.724
0.725
0.726
0.726
0.727
0.728
0.729
0.730
0.730
0.731
0.732
0.733
0.734
0.734
0.735
0.736
0.737
0.738
0.738
0.739
0.740
0.741
0.742
0.742
0.743
0.744
0.745
0.746
0.746
0.747
0.748
0.749
0.750
0.750
0.751
0.752
0.753
0.754
0.754
0.755
0.756
0.757
0.758
0.758
0.759
0.760
0.761
0.762
0.762
0.763
0.764
0.765
0.766
0.766
0.767
0.768
0.769
0.770
0.770
0.771
0.772
0.773
0.774
0.774
0.775
0.776
0.777
0.778
0.778
0.779
0.780
0.781
0.782
0.782
0.783
0.784
0.785
0.786
0.786
0.787
0.788
0.789
0.790
0.790
0.791
0.792
0.793
0.794
0.794
0.795
0.796
0.797
0.798
0.798
0.799
0.800
0.801
0.802
0.802
0.803
0.804
0.805
0.806
0.806
0.807
0.808
0.809
0.810
0.810
0.811
0.812
0.813
0.814
0.814
0.815
0.816
0.817
0.818
0.818
0.819
0.820
0.821
0.822
0.822
0.823
0.824
0.825
0.826
0.826
0.827
0.828
0.829
0.830
0.830
0.831
0.832
0.833
0.834
0.834
0.835
0.836
0.837
0.838
0.838
0.839
0.840
0.841
0.842
0.842
0.843
0.844
0.845
0.846
0.846
0.847
0.848
0.849
0.850
0.850
0.851
0.852
0.853
0.854
0.854
0.855
0.856
0.857
0.858
0.858
0.859
0.860
0.861
0.862
0.862
0.863
0.864
0.865
0.866
0.866
0.867
0.868
0.869
0.870
0.870
0.871
0.872
0.873
0.874
0.874
0.875
0.876
0.877
0.878
0.878
0.879
0.880
0.881
0.882
0.882
0.883
0.884
0.885
0.886
0.886
0.887
0.888
0.889
0.890
0.890
0.891
0.892
0.893
0.894
0.894
0.895
0.896
0.897
0.898
0.898
0.899
0.900
0.901
0.902
0.902
0.903
0.904
0.905
0.906
0.906
0.907
0.908
0.909
0.910
0.910
0.911
0.912
0.913
0.914
0.914
0.915
0.916
0.917
0.918
0.918
0.919
0.920
0.921
0.922
0.922
0.923
0.924
0.925
0.926
0.926
0.927
0.928
0.929
0.930
0.930
0.931
0.932
0.933
0.934
0.934
0.935
0.936
0.937
0.938
0.938
0.939
0.940
0.941
0.942
0.942
0.943
0.944
0.945
0.946
0.946
0.947
0.948
0.949
0.950
0.950
0.951
0.952
0.953
0.954
0.954
0.955
0.956
0.957
0.958
0.958
0.959
0.960
0.961
0.962
0.962
0.963
0.964
0.965
0.966
0.966
0.967
0.968
0.969
0.970
0.970
0.971
0.972
0.973
0.974
0.974
0.975
0.976
0.977
0.978
0.978
0.979
0.980
0.981
0.982
0.982
0.983
0.984
0.985
0.986
0.986
0.987
0.988
0.989
0.990
0.990
0.991
0.992
0.993
0.994
0.994
0.995
0.996
0.997
0.998
0.998
0.999
1.000
1.001
1.002
1.002
1.003
1.004
1.005
1.006
1.006
1.007
1.008
1.009
1.010
1.010
1.011
1.012
1.013
1.014
1.014
1.015
1.016
1.017
1.018
1.018
1.019
1.020
1.021
1.022
1.022
1.023
1.024
1.025
1.026
1.026
1.027
1.028
1.029
1.030
1.030
1.031
1.032
1.033
1.034
1.034
1.035
1.036
1.037
1.038
1.038
1.039
1.040
1.041
1.042
1.042
1.043
1.044
1.045
1.046
1.046
1.047
1.048
1.049
1.050
1.050
1.051
1.052
1.053
1.054
1.054
1.055
1.056
1.057
1.058
1.058
1.059
1.060
1.061
1.062
1.062
1.063
1.064
1.065
1.066
1.066
1.067
1.068
1.069
1.070
1.070
1.071
1.072
1.073
1.074
1.074
1.075
1.076
1.077
1.078
1.078
1.079
1.080
1.081
1.082
1.082
1.083
1.084
1.085
1.086
1.086
1.087
1.088
1.089
1.090
1.090
1.091
1.092
1.093
1.094
1.094
1.095
1.096
1.097
1.098
1.098
1.099
1.100
1.101
1.102
1.102
1.103
1.104
1.105
1.106
1.106
1.107
1.108
1.109
1.110
1.110
1.111
1.112
1.113
1.114
1.114
1.115
1.116
1.117
1.118
1.118
1.119
1.120
1.121
1.122
1.122
1.123
1.124
1.125
1.126
1.126
1.127
1.128
1.129
1.130
1.130
1.131
1.132
1.133
1.134
1.134
1.135
1.136
1.137
1.138
1.138
1.139
1.140
1.141
1.142
1.142
1.143
1.144
1.145
1.146
1.146
1.147
1.148
1.149
1.150
1.150
1.151
1.152
1.153
1.154
1.154
1.155
1.156
1.157
1.158
1.158
1.159
1.160
1.161
1.162
1.162
1.163
1.164
1.165
1.166
1.166
1.167
1.168
1.169
1.170
1.170
1.171
1.172
1.173
1.174
1.174
1.175
1.176
1.177
1.178
1.178
1.179
1.180
1.181
1.182
1.182
1.183
1.184
1.185
1.186
1.186
1.187
1.188
1.189
1.190
1.190
1.191
1.192
1.193
1.194
1.194
1.195
1.196
1.197
1.198
1.198
1.199
1.200
1.201
1.202
1.202
1.203
1.204
1.205
1.206
1.206
1.207
1.208
1.209
1.210
1.210
1.211
1.212
1.213
1.214
1.214
1.215
1.216
1.217
1.218
1.218
1.219
1.220
1.221
1.222
1.222
1.223
1.224
1.225
1.226
1.226
1.227
1.228
1.229
1.230
1.230
1.231
1.232
1.233
1.234
1.234
1.235
1.236
1.237
1.238
1.238
1.239
1.240
1.241
1.242
1.242
1.243
1.244
1.245
1.246
1.246
1.247
1.248
1.249
1.250
1.250
1.251
1.252
1.253
1.254
1.254
1.255
1.256
1.257
1.258
1.258
1.259
1.260
1.261
1.262
1.262
1.263
1.264
1.265
1.266
1.266
1.267
1.268
1.269
1.270
1.270
1.271
1.272
1.273
1.274
1.274
1.275
1.276
1.277
1.278
1.278
1.279
1.280
1.281
1.282
1.282
1.283
1.284
1.285
1.286
1.286
1.287
1.288
1.289
1.290
1.290
1.291
1.292
1.293
1.294
1.294
1.295
1.296
1.297
1.298
1.298
1.299
1.300
1.301
1.302
1.302
1.303
1.304
1.305
1.306
1.306
1.307
1.308
1.309
1.310
1.310
1.311
1.312
1.313
1.314
1.314
1.315
1.316
1.317
1.318
1.318
1.319
1.320
1.321
1.322
1.322
1.323
1.324
1.325
1.326
1.326
1.327
1.328
1.329
1.330
1.330
1.331
1.332
1.333
1.334
1.334
1.335
1.336
1.337
1.338
1.338
1.339
1.340
1.341
1.342
1.342
1.343
1.344
1.345
1.346
1.346
1.347
1.348
1.349
1.350
1.350
1.351
1.352
1.353
1.354
1.354
1.355
1.356
1.357
1.358
1.358
1.359
1.360
1.361
1.362
1.362
1.363
1.364
1.365
1.366
1.366
1.367
1.368
1.369
1.370
1.370
1.371
1.372
1.373
1.374
1.374
1.375
1.376
1.377
1.378
1.378
1.379
1.380
1.381
1.382
1.382
1.383
1.384
1.385
1.386
1.386
1.387
1.388
1.389
1.390
1.390
1.391
1.392
1.393
1.394
1.394
1.395
1.396
1.397
1.397
];
vp=[0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.01
0.02
0.03
0.04
0.05
0.07
0.08
0.10
0.12
0.14
0.17
0.19
0.22
0.25
0.28
0.31
0.35
0.39
0.43
0.47
0.52
0.56
0.61
0.66
0.72
0.77
0.83
0.89
0.96
1.03
1.09
1.17
1.24
1.32
1.40
1.48
1.57
1.66
1.75
1.84
1.94
2.04
2.14
2.25
2.36
2.47
2.59
2.71
2.83
2.96
3.09
3.22
3.36
3.50
3.64
3.79
3.94
4.09
4.25
4.41
4.58
4.75
4.92
5.10
5.28
5.47
5.66
5.85
6.05
6.25
6.45
6.66
6.88
7.09
7.32
7.54
7.77
8.01
8.25
8.49
8.74
8.99
9.25
9.51
9.78
10.05
10.33
10.61
10.89
11.18
11.48
11.77
12.08
12.39
12.70
13.02
13.34
13.67
14.00
14.34
14.68
15.03
15.38
15.74
16.10
16.47
16.84
17.22
17.60
17.98
18.38
18.77
19.17
19.58
19.99
20.41
20.83
21.25
21.68
22.12
22.56
23.00
23.45
23.91
24.37
24.83
25.30
25.78
26.26
26.74
27.23
27.72
28.22
28.72
29.23
29.74
30.26
30.78
31.30
31.83
32.36
32.90
33.45
33.99
34.54
35.10
35.66
36.22
36.79
37.37
37.94
38.52
39.11
39.70
40.29
40.89
41.49
42.09
42.70
43.31
43.93
44.54
45.17
45.79
46.42
47.06
47.69
48.33
48.98
49.62
50.27
50.92
51.58
52.23
52.89
53.55
54.21
54.87
55.53
56.20
56.87
57.54
58.21
58.88
59.55
60.23
60.90
61.58
62.26
62.94
63.62
64.30
64.98
65.66
66.35
67.03
67.72
68.40
69.09
69.78
70.46
71.15
71.84
72.53
73.22
73.91
74.59
75.28
75.97
76.66
77.35
78.04
78.73
79.42
80.11
80.80
81.48
82.17
82.86
83.55
84.23
84.92
85.60
86.29
86.97
87.65
88.34
89.02
89.70
90.38
91.06
91.74
92.41
93.09
93.76
94.44
95.11
95.78
96.45
97.12
97.79
98.46
99.12
99.79
100.45
101.11
101.77
102.43
103.09
103.74
104.40
105.05
105.70
106.35
107.00
107.64
108.29
108.93
109.57
110.21
110.85
111.49
112.12
112.75
113.38
114.01
114.64
115.26
115.89
116.51
117.13
117.75
118.36
118.98
119.59
120.20
120.81
121.41
122.02
122.62
123.22
123.82
124.41
125.01
125.60
126.19
126.78
127.37
127.95
128.53
129.11
129.69
130.27
130.84
131.41
131.98
132.55
133.11
133.68
134.24
134.80
135.36
135.91
136.47
137.02
137.57
138.11
138.66
139.20
139.74
140.28
140.82
141.35
141.88
142.41
142.94
143.47
143.99
144.51
145.03
145.55
146.07
146.58
147.09
147.60
148.11
148.62
149.12
149.62
150.12
150.62
151.12
151.61
152.10
152.59
153.08
153.57
154.05
154.53
155.01
155.49
155.97
156.44
156.92
157.39
157.85
158.32
158.79
159.25
159.71
160.17
160.63
161.08
161.53
161.99
162.44
162.88
163.33
163.77
164.22
164.66
165.10
165.53
165.97
166.40
166.84
167.27
167.69
168.12
168.54
168.97
169.39
169.81
170.23
170.64
171.06
171.47
171.88
172.29
172.70
173.10
173.51
173.91
174.31
174.71
175.11
175.50
175.90
176.29
176.68
177.07
177.46
177.85
178.23
178.62
179.00
179.38
179.76
180.13
180.51
180.88
181.26
181.63
182.00
182.36
182.73
183.09
183.46
183.82
184.18
184.54
184.90
185.25
185.61
185.96
186.31
186.66
187.01
187.36
187.70
188.05
188.39
188.73
189.07
189.41
189.75
190.09
190.42
190.75
191.09
191.42
191.75
192.08
192.40
192.73
193.05
193.37
193.70
194.02
194.33
194.65
194.97
195.28
195.60
195.91
196.22
196.53
196.84
197.15
197.45
197.76
198.06
198.36
198.67
198.97
199.27
199.56
199.86
200.15
200.45
200.74
201.03
201.32
201.61
201.90
202.19
202.47
202.76
203.04
203.33
203.61
203.89
204.17
204.45
204.72
205.00
205.27
205.55
205.82
206.09
206.36
206.63
206.90
207.17
207.43
207.70
207.96
208.22
208.49
208.75
209.01
209.27
209.52
209.78
210.04
210.29
210.55
210.80
211.05
211.30
211.55
211.80
212.05
212.30
212.54
212.79
213.03
213.27
213.52
213.76
214.00
214.24
214.48
214.71
214.95
215.18
215.42
215.65
215.89
216.12
216.35
216.58
216.81
217.04
217.27
217.49
217.72
217.94
218.17
218.39
218.61
218.83
219.05
219.27
219.49
219.71
219.93
220.15
220.36
220.58
220.79
221.00
221.22
221.43
221.64
221.85
222.06
222.27
222.47
222.68
222.89
223.09
223.30
223.50
223.70
223.90
224.11
224.31
224.51
224.70
224.90
225.10
225.30
225.49
225.69
225.88
226.08
226.27
226.46
226.65
226.85
227.04
227.23
227.41
227.60
227.79
227.98
228.16
228.35
228.53
228.72
228.90
229.08
229.26
229.45
229.63
229.81
229.99
230.16
230.34
230.52
230.70
230.87
231.05
231.22
231.40
231.57
231.74
231.91
232.08
232.26
232.43
232.60
232.76
232.93
233.10
233.27
233.43
233.60
233.76
233.93
234.09
234.26
234.42
234.58
234.74
234.90
235.06
235.22
235.38
235.54
235.70
235.86
236.02
236.17
236.33
236.48
236.64
236.79
236.94
237.10
237.25
237.40
237.55
237.70
237.85
238.00
238.15
238.30
238.45
238.60
238.75
238.89
239.04
239.18
239.33
239.47
239.62
239.76
239.90
240.05
240.19
240.33
240.47
240.61
240.75
240.89
241.03
241.17
241.30
241.44
241.58
241.71
241.85
241.99
242.12
242.25
242.39
242.52
242.66
242.79
242.92
243.05
243.18
243.31
243.44
243.57
243.70
243.83
243.96
244.09
244.21
244.34
244.47
244.59
244.72
244.85
244.97
245.09
245.22
245.34
245.46
245.59
245.71
245.83
245.95
246.07
246.19
246.31
246.43
246.55
246.67
246.79
246.91
247.03
247.14
247.26
247.38
247.49
247.61
247.72
247.84
247.95
248.06
248.18
248.29
248.40
248.52
248.63
248.74
248.85
248.96
249.07
249.18
249.29
249.40
249.51
249.62
249.73
249.83
249.94
250.05
250.15
250.26
250.37
250.47
250.58
250.68
250.79
250.89
250.99
251.10
251.20
251.30
251.40
251.51
251.61
251.71
251.81
251.91
252.01
252.11
252.21
252.31
252.41
252.51
252.60
252.70
252.80
252.90
252.99
253.09
253.19
253.28
253.38
253.47
253.57
253.66
253.75
253.85
253.94
254.03
254.13
254.22
254.31
254.40
254.50
254.59
254.68
254.77
254.86
254.95
255.04
255.13
255.22
255.31
255.39
255.48
255.57
255.66
255.74
255.83
255.92
256.00
256.09
256.18
256.26
256.35
256.43
256.52
256.60
256.68
256.77
256.85
256.93
257.02
257.10
257.18
257.26
257.35
257.43
257.51
257.59
257.67
257.75
257.83
257.91
257.99
258.07
258.15
258.23
258.30
258.38
258.46
258.54
258.62
258.69
258.77
258.85
258.92
259.00
259.07
259.15
259.22
259.30
259.37
259.45
259.52
259.60
259.67
259.74
259.82
259.89
259.96
260.04
260.11
260.18
260.25
260.32
260.39
260.47
260.54
260.61
260.68
260.75
260.82
260.89
260.96
261.02
261.09
261.16
261.23
261.30
261.37
261.43
261.50
261.57
261.64
261.70
261.77
261.83
261.90
261.97
262.03
262.10
262.16
262.23
262.29
262.36
262.42
262.49
262.55
262.61
262.68
262.74
262.80
262.86
262.93
262.99
263.05
263.11
263.17
263.24
263.30
263.36
263.42
263.48
263.54
263.60
263.66
263.72
263.78
263.84
263.90
263.96
264.02
264.07
264.13
264.19
264.25
264.31
264.36
264.42
264.48
264.54
264.59
264.65
264.70
264.76
264.82
264.87
264.93
264.98
265.04
265.09
265.15
265.20
265.26
265.31
265.37
265.42
265.47
265.53
265.58
265.63
265.69
265.74
265.79
265.84
265.90
265.95
266.00
266.05
266.10
266.15
266.21
266.26
266.31
266.36
266.41
266.46
266.51
266.56
266.61
266.66
266.71
266.76
266.80
266.85
266.90
266.95
267.00
267.05
267.09
267.14
267.19
267.24
267.28
267.33
267.38
267.43
267.47
267.52
267.56
267.61
267.66
267.70
267.75
267.79
267.84
267.88
267.93
267.97
268.02
268.06
268.11
268.15
268.19
268.24
268.28
268.33
268.37
268.41
268.46
268.50
268.54
268.58
268.63
268.67
268.71
268.75
268.79
268.84
268.88
268.92
268.96
269.00
269.04
269.08
269.12
269.16
269.20
269.24
269.28
269.32
269.36
269.40
269.44
269.48
269.52
269.56
269.60
269.64
269.68
269.72
269.75
269.79
269.83
269.87
269.91
269.94
269.98
270.02
270.06
270.09
270.13
270.17
270.20
270.24
270.28
270.31
270.35
270.38
270.42
270.45
270.49
270.53
270.56
270.60
270.63
270.67
270.70
270.74
270.77
270.80
270.84
270.87
270.91
270.94
270.97
271.01
271.04
271.07
271.11
271.14
271.17
271.21
271.24
271.27
271.30
271.34
271.37
271.40
271.43
271.46
271.50
271.53
271.56
271.59
271.62
271.65
271.68
271.71
271.75
271.78
271.81
271.84
271.87
271.90
271.93
271.96
271.99
272.02
272.05
272.08
272.10
272.13
272.16
272.19
272.22
272.25
272.28
272.31
272.34
272.36
272.39
272.42
272.45
272.48
272.50
272.53
272.56
272.59
272.61
272.64
272.67
272.69
272.72
272.75
272.77
272.80
272.83
272.85
272.88
272.91
272.93
272.96
272.98
273.01
273.03
273.06
273.08
273.11
273.13
273.16
273.18
273.21
273.23
273.26
273.28
273.31
273.33
273.36
273.38
273.40
273.43
273.45
273.47
273.50
273.52
273.55
273.57
273.59
273.61
273.64
273.66
273.68
273.71
273.73
273.75
273.77
273.80
273.82
273.84
273.86
273.88
273.90
273.93
273.95
273.97
273.99
274.01
274.03
274.05
274.08
274.10
274.12
274.14
274.16
274.18
274.20
274.22
274.24
274.26
274.28
274.30
274.32
274.34
274.36
274.38
274.40
274.42
274.44
274.46
274.48
274.49
274.51
274.53
274.55
274.57
274.59
274.61
274.62
274.64
274.66
274.68
274.70
274.72
274.73
274.75
274.77
274.79
274.80
274.82
274.84
274.86
274.87
274.89
274.91
274.92
274.94
274.96
274.97
274.99
275.01
275.02
275.04
275.06
275.07
275.09
275.11
275.12
275.14
275.15
275.17
275.18
275.20
275.22
275.23
275.25
275.26
275.28
275.29
275.31
275.32
275.34
275.35
275.37
275.38
275.39
275.41
275.42
275.44
275.45
275.47
275.48
275.49
275.51
275.52
275.53
275.55
275.56
275.58
275.59
275.60
275.62
275.63
275.64
275.65
275.67
275.68
275.69
275.71
275.72
275.73
275.74
275.76
275.77
275.78
275.79
275.80
275.82
275.83
275.84
275.85
275.86
275.88
275.89
275.90
275.91
275.92
275.93
275.94
275.96
275.97
275.98
275.99
276.00
276.01
276.02
276.03
276.04
276.05
276.06
276.07
276.08
276.09
276.11
276.12
276.13
276.14
276.15
276.16
276.16
276.17
276.18
276.19
276.20
276.21
276.22
276.23
276.24
276.25
276.26
276.27
276.28
276.29
276.30
276.30
276.31
276.32
276.33
276.34
276.35
276.36
276.36
276.37
276.38
276.39
276.40
276.40
276.41
276.42
276.43
276.44
276.44
276.45
276.46
276.47
276.47
276.48
276.49
276.50
276.50
276.51
276.52
276.52
276.53
276.54
276.54
276.55
276.56
276.56
276.57
276.58
276.58
276.59
276.60
276.60
276.61
276.62
276.62
276.63
276.63
276.64
276.65
276.65
276.66
276.66
276.67
276.67
276.68
276.68
276.69
276.70
276.70
276.71
276.71
276.72
276.72
276.73
276.73
276.74
276.74
276.75
276.75
276.76
276.76
276.76
276.77
276.77
276.78
276.78
276.79
276.79
276.79
276.80
276.80
276.81
276.81
276.81
276.82
276.82
276.83
276.83
276.83
276.84
276.84
276.84
276.85
276.85
276.85
276.86
276.86
276.86
276.87
276.87
276.87
276.87
276.88
276.88
276.88
276.89
276.89
276.89
276.89
276.90
276.90
276.90
276.90
276.91
276.91
276.91
276.91
276.91
276.92
276.92
276.92
276.92
276.92
276.93
276.93
276.93
276.93
276.93
276.93
276.94
276.94
276.94
276.94
276.94
276.94
276.94
276.94
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.94
276.94
276.94
276.94
276.94
276.94
276.94
276.94
276.93
276.93
276.93
276.93
276.93
276.93
276.93
276.92
276.92
276.92
276.92
276.92
276.91
276.91
276.91
276.91
276.91
276.90
276.90
276.90
276.90
276.90
276.89
276.89
276.89
276.89
276.88
276.88
276.88
276.88
276.87
276.87
276.87
276.86
276.86
276.86
276.86
276.85
276.85
276.85
276.84
276.84
276.84
276.83
276.83
276.83
276.83
276.82
276.82
276.81
276.81
276.81
276.80
276.80
276.80
276.79
276.79
276.79
276.78
276.78
276.77
276.77
276.77
276.76
276.76
276.75
276.75
276.75
276.74
276.74
276.73
276.73
276.73
276.72
276.72
276.71
276.71
276.70
276.70
276.69
276.69
276.68
276.68
276.68
276.67
276.67
276.66
276.66
276.65
276.65
276.64
276.64
276.63
276.63
276.62
276.62
276.61
276.60
276.60
276.59
276.59
276.58
276.58
276.57
276.57
276.56
276.56
276.55
276.54
276.54
276.53
276.53
276.52
276.52
276.51
276.50
276.50
276.49
276.49
276.48
276.47
276.47
276.46
276.46
276.45
276.44
276.44
276.43
276.42
276.42
276.41
276.40
276.40
276.39
276.39
276.38
276.37
276.37
276.36
276.35
276.35
276.34
276.33
276.32
276.32
276.31
276.30
276.30
276.29
276.28
276.28
276.27
276.26
276.25
276.25
276.24
276.23
276.23
276.22
276.21
276.20
276.20
276.19
276.18
276.17
276.17
276.16
276.15
276.14
276.13
276.13
276.12
276.11
276.10
276.10
276.09
276.08
276.07
276.06
276.06
276.05
276.04
276.03
276.02
276.02
276.01
276.00
275.99
275.98
275.97
275.97
275.96
275.95
275.94
275.94
];
Giulio Rossi
Giulio Rossi le 10 Fév 2021

0 votes

I have those 2 vectors posted below, with values recorded from experimental measurements. when I do the gradient (vp,t) it keeps on giving me the aforementioned plot, with all these kind of "spikes". How can i solve the problem?
Another question...How can I integrate the velocity respect to time using the 2 vectors? matlab promps an error telling Vp is not a function but an array.
Thanks everyone for your kind help.
t=[0.000
0.001
0.002
0.002
0.003
0.004
0.005
0.006
0.006
0.007
0.008
0.009
0.010
0.010
0.011
0.012
0.013
0.014
0.014
0.015
0.016
0.017
0.018
0.018
0.019
0.020
0.021
0.022
0.022
0.023
0.024
0.025
0.026
0.026
0.027
0.028
0.029
0.030
0.030
0.031
0.032
0.033
0.034
0.034
0.035
0.036
0.037
0.038
0.038
0.039
0.040
0.041
0.042
0.042
0.043
0.044
0.045
0.046
0.046
0.047
0.048
0.049
0.050
0.050
0.051
0.052
0.053
0.054
0.054
0.055
0.056
0.057
0.058
0.058
0.059
0.060
0.061
0.062
0.062
0.063
0.064
0.065
0.066
0.066
0.067
0.068
0.069
0.070
0.070
0.071
0.072
0.073
0.074
0.074
0.075
0.076
0.077
0.078
0.078
0.079
0.080
0.081
0.082
0.082
0.083
0.084
0.085
0.086
0.086
0.087
0.088
0.089
0.090
0.090
0.091
0.092
0.093
0.094
0.094
0.095
0.096
0.097
0.098
0.098
0.099
0.100
0.101
0.102
0.102
0.103
0.104
0.105
0.106
0.106
0.107
0.108
0.109
0.110
0.110
0.111
0.112
0.113
0.114
0.114
0.115
0.116
0.117
0.118
0.118
0.119
0.120
0.121
0.122
0.122
0.123
0.124
0.125
0.126
0.126
0.127
0.128
0.129
0.130
0.130
0.131
0.132
0.133
0.134
0.134
0.135
0.136
0.137
0.138
0.138
0.139
0.140
0.141
0.142
0.142
0.143
0.144
0.145
0.146
0.146
0.147
0.148
0.149
0.150
0.150
0.151
0.152
0.153
0.154
0.154
0.155
0.156
0.157
0.158
0.158
0.159
0.160
0.161
0.162
0.162
0.163
0.164
0.165
0.166
0.166
0.167
0.168
0.169
0.170
0.170
0.171
0.172
0.173
0.174
0.174
0.175
0.176
0.177
0.178
0.178
0.179
0.180
0.181
0.182
0.182
0.183
0.184
0.185
0.186
0.186
0.187
0.188
0.189
0.190
0.190
0.191
0.192
0.193
0.194
0.194
0.195
0.196
0.197
0.198
0.198
0.199
0.200
0.201
0.202
0.202
0.203
0.204
0.205
0.206
0.206
0.207
0.208
0.209
0.210
0.210
0.211
0.212
0.213
0.214
0.214
0.215
0.216
0.217
0.218
0.218
0.219
0.220
0.221
0.222
0.222
0.223
0.224
0.225
0.226
0.226
0.227
0.228
0.229
0.230
0.230
0.231
0.232
0.233
0.234
0.234
0.235
0.236
0.237
0.238
0.238
0.239
0.240
0.241
0.242
0.242
0.243
0.244
0.245
0.246
0.246
0.247
0.248
0.249
0.250
0.250
0.251
0.252
0.253
0.254
0.254
0.255
0.256
0.257
0.258
0.258
0.259
0.260
0.261
0.262
0.262
0.263
0.264
0.265
0.266
0.266
0.267
0.268
0.269
0.270
0.270
0.271
0.272
0.273
0.274
0.274
0.275
0.276
0.277
0.278
0.278
0.279
0.280
0.281
0.282
0.282
0.283
0.284
0.285
0.286
0.286
0.287
0.288
0.289
0.290
0.290
0.291
0.292
0.293
0.294
0.294
0.295
0.296
0.297
0.298
0.298
0.299
0.300
0.301
0.302
0.302
0.303
0.304
0.305
0.306
0.306
0.307
0.308
0.309
0.310
0.310
0.311
0.312
0.313
0.314
0.314
0.315
0.316
0.317
0.318
0.318
0.319
0.320
0.321
0.322
0.322
0.323
0.324
0.325
0.326
0.326
0.327
0.328
0.329
0.330
0.330
0.331
0.332
0.333
0.334
0.334
0.335
0.336
0.337
0.338
0.338
0.339
0.340
0.341
0.342
0.342
0.343
0.344
0.345
0.346
0.346
0.347
0.348
0.349
0.350
0.350
0.351
0.352
0.353
0.354
0.354
0.355
0.356
0.357
0.358
0.358
0.359
0.360
0.361
0.362
0.362
0.363
0.364
0.365
0.366
0.366
0.367
0.368
0.369
0.370
0.370
0.371
0.372
0.373
0.374
0.374
0.375
0.376
0.377
0.378
0.378
0.379
0.380
0.381
0.382
0.382
0.383
0.384
0.385
0.386
0.386
0.387
0.388
0.389
0.390
0.390
0.391
0.392
0.393
0.394
0.394
0.395
0.396
0.397
0.398
0.398
0.399
0.400
0.401
0.402
0.402
0.403
0.404
0.405
0.406
0.406
0.407
0.408
0.409
0.410
0.410
0.411
0.412
0.413
0.414
0.414
0.415
0.416
0.417
0.418
0.418
0.419
0.420
0.421
0.422
0.422
0.423
0.424
0.425
0.426
0.426
0.427
0.428
0.429
0.430
0.430
0.431
0.432
0.433
0.434
0.434
0.435
0.436
0.437
0.438
0.438
0.439
0.440
0.441
0.442
0.442
0.443
0.444
0.445
0.446
0.446
0.447
0.448
0.449
0.450
0.450
0.451
0.452
0.453
0.454
0.454
0.455
0.456
0.457
0.458
0.458
0.459
0.460
0.461
0.462
0.462
0.463
0.464
0.465
0.466
0.466
0.467
0.468
0.469
0.470
0.470
0.471
0.472
0.473
0.474
0.474
0.475
0.476
0.477
0.478
0.478
0.479
0.480
0.481
0.482
0.482
0.483
0.484
0.485
0.486
0.486
0.487
0.488
0.489
0.490
0.490
0.491
0.492
0.493
0.494
0.494
0.495
0.496
0.497
0.498
0.498
0.499
0.500
0.501
0.502
0.502
0.503
0.504
0.505
0.506
0.506
0.507
0.508
0.509
0.510
0.510
0.511
0.512
0.513
0.514
0.514
0.515
0.516
0.517
0.518
0.518
0.519
0.520
0.521
0.522
0.522
0.523
0.524
0.525
0.526
0.526
0.527
0.528
0.529
0.530
0.530
0.531
0.532
0.533
0.534
0.534
0.535
0.536
0.537
0.538
0.538
0.539
0.540
0.541
0.542
0.542
0.543
0.544
0.545
0.546
0.546
0.547
0.548
0.549
0.550
0.550
0.551
0.552
0.553
0.554
0.554
0.555
0.556
0.557
0.558
0.558
0.559
0.560
0.561
0.562
0.562
0.563
0.564
0.565
0.566
0.566
0.567
0.568
0.569
0.570
0.570
0.571
0.572
0.573
0.574
0.574
0.575
0.576
0.577
0.578
0.578
0.579
0.580
0.581
0.582
0.582
0.583
0.584
0.585
0.586
0.586
0.587
0.588
0.589
0.590
0.590
0.591
0.592
0.593
0.594
0.594
0.595
0.596
0.597
0.598
0.598
0.599
0.600
0.601
0.602
0.602
0.603
0.604
0.605
0.606
0.606
0.607
0.608
0.609
0.610
0.610
0.611
0.612
0.613
0.614
0.614
0.615
0.616
0.617
0.618
0.618
0.619
0.620
0.621
0.622
0.622
0.623
0.624
0.625
0.626
0.626
0.627
0.628
0.629
0.630
0.630
0.631
0.632
0.633
0.634
0.634
0.635
0.636
0.637
0.638
0.638
0.639
0.640
0.641
0.642
0.642
0.643
0.644
0.645
0.646
0.646
0.647
0.648
0.649
0.650
0.650
0.651
0.652
0.653
0.654
0.654
0.655
0.656
0.657
0.658
0.658
0.659
0.660
0.661
0.662
0.662
0.663
0.664
0.665
0.666
0.666
0.667
0.668
0.669
0.670
0.670
0.671
0.672
0.673
0.674
0.674
0.675
0.676
0.677
0.678
0.678
0.679
0.680
0.681
0.682
0.682
0.683
0.684
0.685
0.686
0.686
0.687
0.688
0.689
0.690
0.690
0.691
0.692
0.693
0.694
0.694
0.695
0.696
0.697
0.698
0.698
0.699
0.700
0.701
0.702
0.702
0.703
0.704
0.705
0.706
0.706
0.707
0.708
0.709
0.710
0.710
0.711
0.712
0.713
0.714
0.714
0.715
0.716
0.717
0.718
0.718
0.719
0.720
0.721
0.722
0.722
0.723
0.724
0.725
0.726
0.726
0.727
0.728
0.729
0.730
0.730
0.731
0.732
0.733
0.734
0.734
0.735
0.736
0.737
0.738
0.738
0.739
0.740
0.741
0.742
0.742
0.743
0.744
0.745
0.746
0.746
0.747
0.748
0.749
0.750
0.750
0.751
0.752
0.753
0.754
0.754
0.755
0.756
0.757
0.758
0.758
0.759
0.760
0.761
0.762
0.762
0.763
0.764
0.765
0.766
0.766
0.767
0.768
0.769
0.770
0.770
0.771
0.772
0.773
0.774
0.774
0.775
0.776
0.777
0.778
0.778
0.779
0.780
0.781
0.782
0.782
0.783
0.784
0.785
0.786
0.786
0.787
0.788
0.789
0.790
0.790
0.791
0.792
0.793
0.794
0.794
0.795
0.796
0.797
0.798
0.798
0.799
0.800
0.801
0.802
0.802
0.803
0.804
0.805
0.806
0.806
0.807
0.808
0.809
0.810
0.810
0.811
0.812
0.813
0.814
0.814
0.815
0.816
0.817
0.818
0.818
0.819
0.820
0.821
0.822
0.822
0.823
0.824
0.825
0.826
0.826
0.827
0.828
0.829
0.830
0.830
0.831
0.832
0.833
0.834
0.834
0.835
0.836
0.837
0.838
0.838
0.839
0.840
0.841
0.842
0.842
0.843
0.844
0.845
0.846
0.846
0.847
0.848
0.849
0.850
0.850
0.851
0.852
0.853
0.854
0.854
0.855
0.856
0.857
0.858
0.858
0.859
0.860
0.861
0.862
0.862
0.863
0.864
0.865
0.866
0.866
0.867
0.868
0.869
0.870
0.870
0.871
0.872
0.873
0.874
0.874
0.875
0.876
0.877
0.878
0.878
0.879
0.880
0.881
0.882
0.882
0.883
0.884
0.885
0.886
0.886
0.887
0.888
0.889
0.890
0.890
0.891
0.892
0.893
0.894
0.894
0.895
0.896
0.897
0.898
0.898
0.899
0.900
0.901
0.902
0.902
0.903
0.904
0.905
0.906
0.906
0.907
0.908
0.909
0.910
0.910
0.911
0.912
0.913
0.914
0.914
0.915
0.916
0.917
0.918
0.918
0.919
0.920
0.921
0.922
0.922
0.923
0.924
0.925
0.926
0.926
0.927
0.928
0.929
0.930
0.930
0.931
0.932
0.933
0.934
0.934
0.935
0.936
0.937
0.938
0.938
0.939
0.940
0.941
0.942
0.942
0.943
0.944
0.945
0.946
0.946
0.947
0.948
0.949
0.950
0.950
0.951
0.952
0.953
0.954
0.954
0.955
0.956
0.957
0.958
0.958
0.959
0.960
0.961
0.962
0.962
0.963
0.964
0.965
0.966
0.966
0.967
0.968
0.969
0.970
0.970
0.971
0.972
0.973
0.974
0.974
0.975
0.976
0.977
0.978
0.978
0.979
0.980
0.981
0.982
0.982
0.983
0.984
0.985
0.986
0.986
0.987
0.988
0.989
0.990
0.990
0.991
0.992
0.993
0.994
0.994
0.995
0.996
0.997
0.998
0.998
0.999
1.000
1.001
1.002
1.002
1.003
1.004
1.005
1.006
1.006
1.007
1.008
1.009
1.010
1.010
1.011
1.012
1.013
1.014
1.014
1.015
1.016
1.017
1.018
1.018
1.019
1.020
1.021
1.022
1.022
1.023
1.024
1.025
1.026
1.026
1.027
1.028
1.029
1.030
1.030
1.031
1.032
1.033
1.034
1.034
1.035
1.036
1.037
1.038
1.038
1.039
1.040
1.041
1.042
1.042
1.043
1.044
1.045
1.046
1.046
1.047
1.048
1.049
1.050
1.050
1.051
1.052
1.053
1.054
1.054
1.055
1.056
1.057
1.058
1.058
1.059
1.060
1.061
1.062
1.062
1.063
1.064
1.065
1.066
1.066
1.067
1.068
1.069
1.070
1.070
1.071
1.072
1.073
1.074
1.074
1.075
1.076
1.077
1.078
1.078
1.079
1.080
1.081
1.082
1.082
1.083
1.084
1.085
1.086
1.086
1.087
1.088
1.089
1.090
1.090
1.091
1.092
1.093
1.094
1.094
1.095
1.096
1.097
1.098
1.098
1.099
1.100
1.101
1.102
1.102
1.103
1.104
1.105
1.106
1.106
1.107
1.108
1.109
1.110
1.110
1.111
1.112
1.113
1.114
1.114
1.115
1.116
1.117
1.118
1.118
1.119
1.120
1.121
1.122
1.122
1.123
1.124
1.125
1.126
1.126
1.127
1.128
1.129
1.130
1.130
1.131
1.132
1.133
1.134
1.134
1.135
1.136
1.137
1.138
1.138
1.139
1.140
1.141
1.142
1.142
1.143
1.144
1.145
1.146
1.146
1.147
1.148
1.149
1.150
1.150
1.151
1.152
1.153
1.154
1.154
1.155
1.156
1.157
1.158
1.158
1.159
1.160
1.161
1.162
1.162
1.163
1.164
1.165
1.166
1.166
1.167
1.168
1.169
1.170
1.170
1.171
1.172
1.173
1.174
1.174
1.175
1.176
1.177
1.178
1.178
1.179
1.180
1.181
1.182
1.182
1.183
1.184
1.185
1.186
1.186
1.187
1.188
1.189
1.190
1.190
1.191
1.192
1.193
1.194
1.194
1.195
1.196
1.197
1.198
1.198
1.199
1.200
1.201
1.202
1.202
1.203
1.204
1.205
1.206
1.206
1.207
1.208
1.209
1.210
1.210
1.211
1.212
1.213
1.214
1.214
1.215
1.216
1.217
1.218
1.218
1.219
1.220
1.221
1.222
1.222
1.223
1.224
1.225
1.226
1.226
1.227
1.228
1.229
1.230
1.230
1.231
1.232
1.233
1.234
1.234
1.235
1.236
1.237
1.238
1.238
1.239
1.240
1.241
1.242
1.242
1.243
1.244
1.245
1.246
1.246
1.247
1.248
1.249
1.250
1.250
1.251
1.252
1.253
1.254
1.254
1.255
1.256
1.257
1.258
1.258
1.259
1.260
1.261
1.262
1.262
1.263
1.264
1.265
1.266
1.266
1.267
1.268
1.269
1.270
1.270
1.271
1.272
1.273
1.274
1.274
1.275
1.276
1.277
1.278
1.278
1.279
1.280
1.281
1.282
1.282
1.283
1.284
1.285
1.286
1.286
1.287
1.288
1.289
1.290
1.290
1.291
1.292
1.293
1.294
1.294
1.295
1.296
1.297
1.298
1.298
1.299
1.300
1.301
1.302
1.302
1.303
1.304
1.305
1.306
1.306
1.307
1.308
1.309
1.310
1.310
1.311
1.312
1.313
1.314
1.314
1.315
1.316
1.317
1.318
1.318
1.319
1.320
1.321
1.322
1.322
1.323
1.324
1.325
1.326
1.326
1.327
1.328
1.329
1.330
1.330
1.331
1.332
1.333
1.334
1.334
1.335
1.336
1.337
1.338
1.338
1.339
1.340
1.341
1.342
1.342
1.343
1.344
1.345
1.346
1.346
1.347
1.348
1.349
1.350
1.350
1.351
1.352
1.353
1.354
1.354
1.355
1.356
1.357
1.358
1.358
1.359
1.360
1.361
1.362
1.362
1.363
1.364
1.365
1.366
1.366
1.367
1.368
1.369
1.370
1.370
1.371
1.372
1.373
1.374
1.374
1.375
1.376
1.377
1.378
1.378
1.379
1.380
1.381
1.382
1.382
1.383
1.384
1.385
1.386
1.386
1.387
1.388
1.389
1.390
1.390
1.391
1.392
1.393
1.394
1.394
1.395
1.396
1.397
1.397
];
vp=[0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.01
0.01
0.02
0.03
0.04
0.05
0.07
0.08
0.10
0.12
0.14
0.17
0.19
0.22
0.25
0.28
0.31
0.35
0.39
0.43
0.47
0.52
0.56
0.61
0.66
0.72
0.77
0.83
0.89
0.96
1.03
1.09
1.17
1.24
1.32
1.40
1.48
1.57
1.66
1.75
1.84
1.94
2.04
2.14
2.25
2.36
2.47
2.59
2.71
2.83
2.96
3.09
3.22
3.36
3.50
3.64
3.79
3.94
4.09
4.25
4.41
4.58
4.75
4.92
5.10
5.28
5.47
5.66
5.85
6.05
6.25
6.45
6.66
6.88
7.09
7.32
7.54
7.77
8.01
8.25
8.49
8.74
8.99
9.25
9.51
9.78
10.05
10.33
10.61
10.89
11.18
11.48
11.77
12.08
12.39
12.70
13.02
13.34
13.67
14.00
14.34
14.68
15.03
15.38
15.74
16.10
16.47
16.84
17.22
17.60
17.98
18.38
18.77
19.17
19.58
19.99
20.41
20.83
21.25
21.68
22.12
22.56
23.00
23.45
23.91
24.37
24.83
25.30
25.78
26.26
26.74
27.23
27.72
28.22
28.72
29.23
29.74
30.26
30.78
31.30
31.83
32.36
32.90
33.45
33.99
34.54
35.10
35.66
36.22
36.79
37.37
37.94
38.52
39.11
39.70
40.29
40.89
41.49
42.09
42.70
43.31
43.93
44.54
45.17
45.79
46.42
47.06
47.69
48.33
48.98
49.62
50.27
50.92
51.58
52.23
52.89
53.55
54.21
54.87
55.53
56.20
56.87
57.54
58.21
58.88
59.55
60.23
60.90
61.58
62.26
62.94
63.62
64.30
64.98
65.66
66.35
67.03
67.72
68.40
69.09
69.78
70.46
71.15
71.84
72.53
73.22
73.91
74.59
75.28
75.97
76.66
77.35
78.04
78.73
79.42
80.11
80.80
81.48
82.17
82.86
83.55
84.23
84.92
85.60
86.29
86.97
87.65
88.34
89.02
89.70
90.38
91.06
91.74
92.41
93.09
93.76
94.44
95.11
95.78
96.45
97.12
97.79
98.46
99.12
99.79
100.45
101.11
101.77
102.43
103.09
103.74
104.40
105.05
105.70
106.35
107.00
107.64
108.29
108.93
109.57
110.21
110.85
111.49
112.12
112.75
113.38
114.01
114.64
115.26
115.89
116.51
117.13
117.75
118.36
118.98
119.59
120.20
120.81
121.41
122.02
122.62
123.22
123.82
124.41
125.01
125.60
126.19
126.78
127.37
127.95
128.53
129.11
129.69
130.27
130.84
131.41
131.98
132.55
133.11
133.68
134.24
134.80
135.36
135.91
136.47
137.02
137.57
138.11
138.66
139.20
139.74
140.28
140.82
141.35
141.88
142.41
142.94
143.47
143.99
144.51
145.03
145.55
146.07
146.58
147.09
147.60
148.11
148.62
149.12
149.62
150.12
150.62
151.12
151.61
152.10
152.59
153.08
153.57
154.05
154.53
155.01
155.49
155.97
156.44
156.92
157.39
157.85
158.32
158.79
159.25
159.71
160.17
160.63
161.08
161.53
161.99
162.44
162.88
163.33
163.77
164.22
164.66
165.10
165.53
165.97
166.40
166.84
167.27
167.69
168.12
168.54
168.97
169.39
169.81
170.23
170.64
171.06
171.47
171.88
172.29
172.70
173.10
173.51
173.91
174.31
174.71
175.11
175.50
175.90
176.29
176.68
177.07
177.46
177.85
178.23
178.62
179.00
179.38
179.76
180.13
180.51
180.88
181.26
181.63
182.00
182.36
182.73
183.09
183.46
183.82
184.18
184.54
184.90
185.25
185.61
185.96
186.31
186.66
187.01
187.36
187.70
188.05
188.39
188.73
189.07
189.41
189.75
190.09
190.42
190.75
191.09
191.42
191.75
192.08
192.40
192.73
193.05
193.37
193.70
194.02
194.33
194.65
194.97
195.28
195.60
195.91
196.22
196.53
196.84
197.15
197.45
197.76
198.06
198.36
198.67
198.97
199.27
199.56
199.86
200.15
200.45
200.74
201.03
201.32
201.61
201.90
202.19
202.47
202.76
203.04
203.33
203.61
203.89
204.17
204.45
204.72
205.00
205.27
205.55
205.82
206.09
206.36
206.63
206.90
207.17
207.43
207.70
207.96
208.22
208.49
208.75
209.01
209.27
209.52
209.78
210.04
210.29
210.55
210.80
211.05
211.30
211.55
211.80
212.05
212.30
212.54
212.79
213.03
213.27
213.52
213.76
214.00
214.24
214.48
214.71
214.95
215.18
215.42
215.65
215.89
216.12
216.35
216.58
216.81
217.04
217.27
217.49
217.72
217.94
218.17
218.39
218.61
218.83
219.05
219.27
219.49
219.71
219.93
220.15
220.36
220.58
220.79
221.00
221.22
221.43
221.64
221.85
222.06
222.27
222.47
222.68
222.89
223.09
223.30
223.50
223.70
223.90
224.11
224.31
224.51
224.70
224.90
225.10
225.30
225.49
225.69
225.88
226.08
226.27
226.46
226.65
226.85
227.04
227.23
227.41
227.60
227.79
227.98
228.16
228.35
228.53
228.72
228.90
229.08
229.26
229.45
229.63
229.81
229.99
230.16
230.34
230.52
230.70
230.87
231.05
231.22
231.40
231.57
231.74
231.91
232.08
232.26
232.43
232.60
232.76
232.93
233.10
233.27
233.43
233.60
233.76
233.93
234.09
234.26
234.42
234.58
234.74
234.90
235.06
235.22
235.38
235.54
235.70
235.86
236.02
236.17
236.33
236.48
236.64
236.79
236.94
237.10
237.25
237.40
237.55
237.70
237.85
238.00
238.15
238.30
238.45
238.60
238.75
238.89
239.04
239.18
239.33
239.47
239.62
239.76
239.90
240.05
240.19
240.33
240.47
240.61
240.75
240.89
241.03
241.17
241.30
241.44
241.58
241.71
241.85
241.99
242.12
242.25
242.39
242.52
242.66
242.79
242.92
243.05
243.18
243.31
243.44
243.57
243.70
243.83
243.96
244.09
244.21
244.34
244.47
244.59
244.72
244.85
244.97
245.09
245.22
245.34
245.46
245.59
245.71
245.83
245.95
246.07
246.19
246.31
246.43
246.55
246.67
246.79
246.91
247.03
247.14
247.26
247.38
247.49
247.61
247.72
247.84
247.95
248.06
248.18
248.29
248.40
248.52
248.63
248.74
248.85
248.96
249.07
249.18
249.29
249.40
249.51
249.62
249.73
249.83
249.94
250.05
250.15
250.26
250.37
250.47
250.58
250.68
250.79
250.89
250.99
251.10
251.20
251.30
251.40
251.51
251.61
251.71
251.81
251.91
252.01
252.11
252.21
252.31
252.41
252.51
252.60
252.70
252.80
252.90
252.99
253.09
253.19
253.28
253.38
253.47
253.57
253.66
253.75
253.85
253.94
254.03
254.13
254.22
254.31
254.40
254.50
254.59
254.68
254.77
254.86
254.95
255.04
255.13
255.22
255.31
255.39
255.48
255.57
255.66
255.74
255.83
255.92
256.00
256.09
256.18
256.26
256.35
256.43
256.52
256.60
256.68
256.77
256.85
256.93
257.02
257.10
257.18
257.26
257.35
257.43
257.51
257.59
257.67
257.75
257.83
257.91
257.99
258.07
258.15
258.23
258.30
258.38
258.46
258.54
258.62
258.69
258.77
258.85
258.92
259.00
259.07
259.15
259.22
259.30
259.37
259.45
259.52
259.60
259.67
259.74
259.82
259.89
259.96
260.04
260.11
260.18
260.25
260.32
260.39
260.47
260.54
260.61
260.68
260.75
260.82
260.89
260.96
261.02
261.09
261.16
261.23
261.30
261.37
261.43
261.50
261.57
261.64
261.70
261.77
261.83
261.90
261.97
262.03
262.10
262.16
262.23
262.29
262.36
262.42
262.49
262.55
262.61
262.68
262.74
262.80
262.86
262.93
262.99
263.05
263.11
263.17
263.24
263.30
263.36
263.42
263.48
263.54
263.60
263.66
263.72
263.78
263.84
263.90
263.96
264.02
264.07
264.13
264.19
264.25
264.31
264.36
264.42
264.48
264.54
264.59
264.65
264.70
264.76
264.82
264.87
264.93
264.98
265.04
265.09
265.15
265.20
265.26
265.31
265.37
265.42
265.47
265.53
265.58
265.63
265.69
265.74
265.79
265.84
265.90
265.95
266.00
266.05
266.10
266.15
266.21
266.26
266.31
266.36
266.41
266.46
266.51
266.56
266.61
266.66
266.71
266.76
266.80
266.85
266.90
266.95
267.00
267.05
267.09
267.14
267.19
267.24
267.28
267.33
267.38
267.43
267.47
267.52
267.56
267.61
267.66
267.70
267.75
267.79
267.84
267.88
267.93
267.97
268.02
268.06
268.11
268.15
268.19
268.24
268.28
268.33
268.37
268.41
268.46
268.50
268.54
268.58
268.63
268.67
268.71
268.75
268.79
268.84
268.88
268.92
268.96
269.00
269.04
269.08
269.12
269.16
269.20
269.24
269.28
269.32
269.36
269.40
269.44
269.48
269.52
269.56
269.60
269.64
269.68
269.72
269.75
269.79
269.83
269.87
269.91
269.94
269.98
270.02
270.06
270.09
270.13
270.17
270.20
270.24
270.28
270.31
270.35
270.38
270.42
270.45
270.49
270.53
270.56
270.60
270.63
270.67
270.70
270.74
270.77
270.80
270.84
270.87
270.91
270.94
270.97
271.01
271.04
271.07
271.11
271.14
271.17
271.21
271.24
271.27
271.30
271.34
271.37
271.40
271.43
271.46
271.50
271.53
271.56
271.59
271.62
271.65
271.68
271.71
271.75
271.78
271.81
271.84
271.87
271.90
271.93
271.96
271.99
272.02
272.05
272.08
272.10
272.13
272.16
272.19
272.22
272.25
272.28
272.31
272.34
272.36
272.39
272.42
272.45
272.48
272.50
272.53
272.56
272.59
272.61
272.64
272.67
272.69
272.72
272.75
272.77
272.80
272.83
272.85
272.88
272.91
272.93
272.96
272.98
273.01
273.03
273.06
273.08
273.11
273.13
273.16
273.18
273.21
273.23
273.26
273.28
273.31
273.33
273.36
273.38
273.40
273.43
273.45
273.47
273.50
273.52
273.55
273.57
273.59
273.61
273.64
273.66
273.68
273.71
273.73
273.75
273.77
273.80
273.82
273.84
273.86
273.88
273.90
273.93
273.95
273.97
273.99
274.01
274.03
274.05
274.08
274.10
274.12
274.14
274.16
274.18
274.20
274.22
274.24
274.26
274.28
274.30
274.32
274.34
274.36
274.38
274.40
274.42
274.44
274.46
274.48
274.49
274.51
274.53
274.55
274.57
274.59
274.61
274.62
274.64
274.66
274.68
274.70
274.72
274.73
274.75
274.77
274.79
274.80
274.82
274.84
274.86
274.87
274.89
274.91
274.92
274.94
274.96
274.97
274.99
275.01
275.02
275.04
275.06
275.07
275.09
275.11
275.12
275.14
275.15
275.17
275.18
275.20
275.22
275.23
275.25
275.26
275.28
275.29
275.31
275.32
275.34
275.35
275.37
275.38
275.39
275.41
275.42
275.44
275.45
275.47
275.48
275.49
275.51
275.52
275.53
275.55
275.56
275.58
275.59
275.60
275.62
275.63
275.64
275.65
275.67
275.68
275.69
275.71
275.72
275.73
275.74
275.76
275.77
275.78
275.79
275.80
275.82
275.83
275.84
275.85
275.86
275.88
275.89
275.90
275.91
275.92
275.93
275.94
275.96
275.97
275.98
275.99
276.00
276.01
276.02
276.03
276.04
276.05
276.06
276.07
276.08
276.09
276.11
276.12
276.13
276.14
276.15
276.16
276.16
276.17
276.18
276.19
276.20
276.21
276.22
276.23
276.24
276.25
276.26
276.27
276.28
276.29
276.30
276.30
276.31
276.32
276.33
276.34
276.35
276.36
276.36
276.37
276.38
276.39
276.40
276.40
276.41
276.42
276.43
276.44
276.44
276.45
276.46
276.47
276.47
276.48
276.49
276.50
276.50
276.51
276.52
276.52
276.53
276.54
276.54
276.55
276.56
276.56
276.57
276.58
276.58
276.59
276.60
276.60
276.61
276.62
276.62
276.63
276.63
276.64
276.65
276.65
276.66
276.66
276.67
276.67
276.68
276.68
276.69
276.70
276.70
276.71
276.71
276.72
276.72
276.73
276.73
276.74
276.74
276.75
276.75
276.76
276.76
276.76
276.77
276.77
276.78
276.78
276.79
276.79
276.79
276.80
276.80
276.81
276.81
276.81
276.82
276.82
276.83
276.83
276.83
276.84
276.84
276.84
276.85
276.85
276.85
276.86
276.86
276.86
276.87
276.87
276.87
276.87
276.88
276.88
276.88
276.89
276.89
276.89
276.89
276.90
276.90
276.90
276.90
276.91
276.91
276.91
276.91
276.91
276.92
276.92
276.92
276.92
276.92
276.93
276.93
276.93
276.93
276.93
276.93
276.94
276.94
276.94
276.94
276.94
276.94
276.94
276.94
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.96
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.95
276.94
276.94
276.94
276.94
276.94
276.94
276.94
276.94
276.93
276.93
276.93
276.93
276.93
276.93
276.93
276.92
276.92
276.92
276.92
276.92
276.91
276.91
276.91
276.91
276.91
276.90
276.90
276.90
276.90
276.90
276.89
276.89
276.89
276.89
276.88
276.88
276.88
276.88
276.87
276.87
276.87
276.86
276.86
276.86
276.86
276.85
276.85
276.85
276.84
276.84
276.84
276.83
276.83
276.83
276.83
276.82
276.82
276.81
276.81
276.81
276.80
276.80
276.80
276.79
276.79
276.79
276.78
276.78
276.77
276.77
276.77
276.76
276.76
276.75
276.75
276.75
276.74
276.74
276.73
276.73
276.73
276.72
276.72
276.71
276.71
276.70
276.70
276.69
276.69
276.68
276.68
276.68
276.67
276.67
276.66
276.66
276.65
276.65
276.64
276.64
276.63
276.63
276.62
276.62
276.61
276.60
276.60
276.59
276.59
276.58
276.58
276.57
276.57
276.56
276.56
276.55
276.54
276.54
276.53
276.53
276.52
276.52
276.51
276.50
276.50
276.49
276.49
276.48
276.47
276.47
276.46
276.46
276.45
276.44
276.44
276.43
276.42
276.42
276.41
276.40
276.40
276.39
276.39
276.38
276.37
276.37
276.36
276.35
276.35
276.34
276.33
276.32
276.32
276.31
276.30
276.30
276.29
276.28
276.28
276.27
276.26
276.25
276.25
276.24
276.23
276.23
276.22
276.21
276.20
276.20
276.19
276.18
276.17
276.17
276.16
276.15
276.14
276.13
276.13
276.12
276.11
276.10
276.10
276.09
276.08
276.07
276.06
276.06
276.05
276.04
276.03
276.02
276.02
276.01
276.00
275.99
275.98
275.97
275.97
275.96
275.95
275.94
275.94
];

Catégories

En savoir plus sur Programming dans Centre d'aide et File Exchange

Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by