(Solved): a) Use the linearity property to find the Laplace transform of \( f(t)=A \cos (\beta t) \). Hint: ...

a) Use the linearity property to find the Laplace transform of \( f(t)=A \cos (\beta t) \). Hint: recall that \( \cos (\theta)=\frac{1}{2}\left(e^{j \theta}+e^{-j \theta}\right) \) b) Compute the Laplace transform of \( v(t) \), when \( \frac{d v(t)}{d t}+6 v(t)=4 u(t), v\left(0^{-}\right)=-3 V \). c) Find the Laplace transform of the following signal \( v(t)=-7 u(t) \), where \( u(t) \) is a step function