Chapter 4.6, Problem 6P

A mass of $4$ kg stretches a spring $8$ cm. The mass is acted on by an external force of $8\sin \left(t/2\right)$ newtons $\left(N\right)$ and moves in a medium that imparts a viscous force of $4N$ when the speed of the mass is $2$ cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of $16$ cm/s, formulate the initial value problem describing the motion of the mass.