(Solved): From the sheet of the Laplace transform review, find the \( F(s) \) for: 1. The ramp function \( f( ...

From the sheet of the Laplace transform review, find the \( F(s) \) for: 1. The ramp function \( f(t)=t \), Write the steps (the solution is \( F(s)=1 / s^{2} \) ). 2. Find \( F(s) \) for \( f(t)=\sin (w t) \), and use the exponential function as described in the sheet. Show the steps of your derivation (the solution is \( F(s)=w / s^{2}+w^{2} \) ). 3. Find \( F(s) \) for \( f(t)=3-4 e^{-2 t} \).