Chapter 12.5, Problem 2AP

(a)

To determine

Find the Laplace transform of the function $t^2{e}^{-at}$ using the appropriate operational transform.

(b)

To determine

Find the Laplace transform of the function $\frac{d}{dt}\left(e^{-at}\sinh \beta t\right)$ using the appropriate operational transform.

(c)

To determine

Find the Laplace transform of the function $t\cos \omega t$  using the appropriate operational transform.