A mass of 1 slug when attached to a spring stretches the spring 2 feet and then comes to rest in the equilibrium

Question

A mass of 1 slug, when attached to a spring, stretches the spring 2 feet and then comes to rest in the equilibrium

position. Starting at t = 0, an external force equal to f(t) = 8 sin(4t) is applied to the system.(In this scenario, the mass is initially at rest in the equilibrium position.) Find the equation of motion if thesurrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity

Running head: [SHORTENED TITLE UP TO 50 CHARACTERS] 1
A mass of 1 slug, when attached to a spring, stretches the spring 2 feet and then comes to rest in
the equilibrium position. Starting at t = 0,…
Math