Efficient Laplace Transform for t*cos(3t) and e^(2t)sin(4t) Functions

[Lucy77]

Find laplace transfom (t-1)cos3t + e^(2t)sin4t

f(t) = t*cos(3*t)
g(t) = -cos(3*t)
h(t) = e2*t*sin(4*t)


int e^(-st) * t* cos(3*t)dt = s^(2)-9/(s^(2)+9)^2
g(t)= -1/(s^2+9)
h(t)= (s-2)/(s-2)^2 +16

am I done and right? Thanks

 

[quantumdude]

The first one is right. The second one is close (you forgot to multiply by 9). The third one looks way off.

In general, L{e^btsin(at)}=a/[(s-b)²+a²]

 

[Lucy77]

Thanks,

The third one should be 4/(s-2)^2+16. Do I have to combine all of these. Am unsure about that part.

Thanks

 

[quantumdude]

You only have to combine them if the problem says so.

Did they ask you to find L{f(t)+g(t)+h(t)}?

If not, then you can leave them seperate.