Derive the transfer functions for the following governing equations of motion:

(a) \(\ddot{x}+2 \dot{x}+4 x=\cos \omega t\)

(b) \(m \ddot{x}+c \dot{x}+k x=A \cos \omega t\)

(c) \(m \ddot{x}+c \dot{x}+k x=A_{1} \cos \omega t+A_{2} \sin \omega t\)

(d) \(m \ddot{x}+k x=u(t), u(t)=1, t \geq 0\)

(e) \(m \ddot{x}+c \dot{x}+k x=e^{-\omega t} \cos \Omega t\).