Laplace Transform Practice Problems: Solving for t and Inverse Transform

[riot]

hi,
i just started doing laplace transform n i have real trouble doing these two questions, anyhelp would be great...

L{te^t(sint)}
L^-1{1/((s^2+1)(s-1)^2)}

 

[J77]

You need to show some working.

Starting with the question may help...

 

[riot]

for the first question t*e^t*sin(t) i got
(2s-2)/((s-1)^2+1)^2
and for the L^-1{1/((s^2+1)(s-1)^2)} i got
(e^s/8)-(s*e^s/4)-(e^-s/8)+(s^2*e^s/4)
...doesnt look right does it?

 

[LeonhardEuler]

The first one is right, let me check the second.

 

[LeonhardEuler]

Oh, the second is definitely not right. When you take the inverse laplace transform you should get a function of t only with no s. How did you try to do it?

 

[riot]

oh yea sorry i mean to write t instead of s..my bad~!
but after looking at it again i got

cos(t)/2 - e^t/2 + te^t/2

i think this one is correct..anyway thanks for all your help :)