ILaplace of transfer function

Hello,

I have this transfer function[1 + 4.632s + 3.576s^2 + 1.104s^3], I need it's ilaplace transform when it is subjected to input=Asin(wt). Matlab gives{66.25487934 dirac(1, t) + 214.5553843 dirac(t) - 318.3731729 cos(3. t)- 623.6661530 sin(3. t)} while if I do it manual it gives{A*sin⍵t+ 4.632*⍵*A*cos⍵t- 3.576*⍵^2*A*sin⍵t- 1.104*⍵^3*A cos⍵t}. If any one can help how I can let matlab give the same as manual results. Thanks

Answer 1

[Star Strider]

I may have miscopid something, but this code:

syms s w t A
tf1 = [1 + 4.632*s + 3.576*s^2 + 1.104*s^3];
input= A * laplace(sin(w*t));
ff1 = laplace(input, t,s)
ff2 = tf1 * ff1
Il1 = simplify(ilaplace(ff2),'steps', 10)

Gives me this result:

Il1 =
(138*A*w*dirac(t))/125 - (A*(447*w^2*(2*sin((t*w)/2)^2 - 1) - 250*sin((t*w)/2)^2 - 579*w*sin(t*w) + 138*w^3*sin(t*w)))/(125*w)

[Bilal Jarrah]

Hi Star, Thanks for quick answer, but my problem is with the dirac(t) I need all results to be sin and cos.

Bilal

[Star Strider]

Just substitute 1 for dirac(t).