Chapter 4.10, Problem 12E

A $2\text{-kg}$ mass is attached to a spring hanging from the ceiling, thereby causing the spring to stretch upon $20cm$ coming to rest at equilibrium. At time $t=0$ the mass is displaced $5\text{ cm}$ below the equilibrium position and released. At this same instant, an external force $F\left(t\right)=0.3\cos tN$ is applied to the system. If the damping constant for the system is $5\text{N-}\text{sec}/\text{m}$, determine the equation of motion for the mass. What is the resonance frequency for the system?