- #1

- 367

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## Homework Statement

4(d

^{2}x/dt

^{2}) +3x = t*e

^{-3t}sin(5t)

## Homework Equations

## The Attempt at a Solution

So I know how to take the Laplace transform and find the function for the Laplace domain:

X(s) = 10(s+3)/(((s+3)

^{2}+25)

^{2})(4s

^{2}+3) + (10s/(4s

^{2}+3)) + (2/(4s

^{2}+3))

But trying to convert 10(s+3)/(((s+3)

^{2}+25)

^{2})(4s

^{2}+3) back into the time domain is giving me a lot of trouble!

Those imaginary roots are really throwing me off. It was suggested to me to use conjugate poles to solve for this part, but I've never learned this method.

Any help is greatly appreciated!

Also not related to the homework question but, is there a fraction button somewhere?? I realize the question is hard to look at when there are so many parenthesis and slashes.