(Solved):   Laplace and Inverse Laplace Transformation (12 points). Clearly state the transformation p ...

 

Laplace and Inverse Laplace Transformation (12 points). Clearly state the
transformation pairs used.

Q2. Laplace and Inverse Laplace Transformation ( 12 points). Clearly state the transformation pairs used. a. For \( \mathrm{X}(\mathrm{s})=(\mathrm{s}-1) / \mathrm{s}(\mathrm{s}+1) \), find \( \mathrm{x}(\mathrm{t}), \mathrm{x}(2 \mathrm{t}), \frac{d}{d t} \mathrm{x}(\mathrm{t}) \). b. Find signal \( \mathrm{x}(\mathrm{t}) \) for \( \mathrm{X}(\mathrm{s})=\frac{s}{\left(s^{2}+4\right)}+\frac{4 s}{\left(s^{2}+4\right)^{2}}+\frac{1}{(s+4)^{2}} \) c. Find \( x(s) \) for \( x(t)=t \sin 3 t+e^{-3 t} \sin 9 t+t e^{-9 t} \)