Consider a spring mass damper system with the following Input-Output model:

\[m \ddot{y}+f \dot{y}+k y=u(t) \text { where } u(t) \text { is a constant, and } \dot{y}(0)=0\]

(a) Find \(Y(s)\), the Laplace transform of the output, \(y(t)\).

(b) For the specific case with the following data

\[m=1, k=2, f=3, y(0)=1 \text { and } u(t)=0 \text {, }\]

find the system response, \(y(t)\).