Consider the equation of motion of a first-order system:

\[0.5 \dot{x}+4 x=f(t)\]

where the forcing function \(f(t)\) is periodic. If the Fourier series representation of \(f(t)\) is given by

\[f(t)=4 \sin 2 t+2 \sin 4 t+\sin 6 t+0.5 \sin 8 t+\ldots\]

a. what is the bandwidth of the system?

b. find the steady-state response of the system considering only those components of \(f(t)\) that lie within the bandwidth of the system.