Chapter 4.5, Problem 43E

A mass–spring system is driven by a sinusoidal external force $g\left(t\right)=5\sin t$. The mass equals 1, the spring constant equals 3, and the damping coefficient equals 4. If the mass is initially located at $y\left(0\right)=1/2$ and at rest, i.e., $y^{\prime }\left(0\right)=0$, find its equation of motion.