Laplace Transforms:

1. Find the Laplace transforms of the given functions.  solution

(a)  \(f(t) = 2e^{-3t}+1+t^2\)  

(b)  \(f(t) = 4 \sin (\sqrt{3}t) - 7 \cos (5t) \)

(c)  \(f(t) = \sinh (3t) - 7 \cosh (5t) \)

(d)  \(f(t) = \sin (3t) - e^{3t} \sin (3t) \)    

2.  Find the Laplace transform of the following function.   solution

(a)  \(f(t) = 2t^3-3t^2-5\)  

(b)  \(f(t) = e^{-5t}+\cos (\sqrt{2}\, t) \)

(c)  \(f(t) = \sin (t/2) -  \sinh (2t) \) 

3. Find the Laplace transform of each of  the following functions.   solution

(a)  \(f(t) = t  e^{3t}\)  

(b)  \(f(t) = t  \cos(2t) \)

(c) \( f(t)=t^2 \sin(3t)\)