Member • Oct 26, 2011

## Laplace Transform : sin^2(wt) question

Q: What is the inverse Laplace transform of {32 / (s(s[SUP]2[/SUP] + 64))} ?

A: sin[SUP]2[/SUP](4t)

The Laplace Look Up Table formula is :

Signal Transform sin[SUP]2[/SUP](w[SUB]0[/SUB]t) 2w[SUB]0[/SUB][SUP]2[/SUP] / (s(s[SUP]2[/SUP] + 4w[SUB]0[/SUB][SUP]2[/SUP]))When I am breaking down this function and I am using the transform equation I can only break down the 64 (since 8[SUP]2[/SUP] = 64) but that 4 right next to it and that 32 is throwing me for a loop.

I really appreciate it if someone can help me understand how the answer is sin[SUP]2[/SUP](4t)