This problem explores the analogy between an RLC electrical circuit and a mass$/$spring$/$damper mechanical system.

Consider a mass$/$spring$/$damper model of a vehicle suspension and a series RLC circuit to study oscillations illustrated

below:

Mechanical oscillation

There is an analogy between spring$-$mass system and $RLC$ circuits given by:

Assume either system has been operating for a long time, that is the system is in steady$-$state, that is$,$ the transient has

disappeared. Use either system to find the steady$-$state output $($mechanical position $u(t)$ or electrical charge $Q(t))$ to an

applied sinusoidal input $($mechanical force $F(t)$ or electrical voltage $E(t))$ given by