double integration of acceleration data with offset

hello there

i want to use the accerleration with offset added to it and then double intgrate using cumtrapz to obtain velocity and position, but when i plot my offset position it doesnt look anywhere near my real position even tho it has only 0.1 offset from integrating acceleration.

here is the code i used

a=0.5 % amplitude
f=5   % frequency
t=linspace(0,10,500);
v0 = a*(2*pi/f)*cos(2*pi/f*t(1)); % initial velocity
p0 = a*sin((2*pi)/f*t(1)); % initial position 
acc= -4*a.*pi^2./f.^2 .* sin(2*pi./f .* t); % accleration data
off_set=0.1;
acc=acc+off_set;
figure (1)
plot(t,acc,'g','linewidth',2);
xlabel('Time (s)')
ylabel('amplitude')
title('accleration')
vel=cumtrapz(t,acc)+v0; % integrated velocity
pos=cumtrapz(t,vel)+p0  % intgrated positon
figure(2)
plot(t,pos,'r-')  % plot the position      
xlabel('Time (s)')
ylabel('amplitude')
title('offset position')

% what my real position look like real position 
pos=a*sin((2*pi)/f*t) % intial position
plot(t,pos,'b-');  % plot for position
title(' real positon')
ylabel('amplitude')
xlabel('time(s)')

i want to be able to add offset to acceleration, and when i double intgrate to get a position with offset, somewhat obtain a plot similar to my real position even tho it has 0.1 offset.

any help would be massivley appreaciated

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[James Tursa]

You put a constant offset into the acceleration, not the position. The result of double integrating a constant is going to be a (1/2)(constant offset)*t.^2 offset in position. I.e., growing position difference with time, not a constant offset position.