Please help me find my initial position and velocity for the following problem that applies second-order differential equations. A mass of 1 slug, when attached to a spring, stretches it 2ft and then comes to rest in the equilibrium position. Starting at t=0, an external force equal to f(t)=8sin4t is applied to the system. Find the equation of motion if the surrounding medium offers a damping force numerically equally to 8 times the instantaneous velocity.

Question

Please help me find my initial position and velocity for the following problem that applies second-order differential equations.  A mass of 1 slug, when attached to a spring, stretches it 2ft and then comes to rest in the equilibrium position. Starting at t=0, an external force equal to f(t)=8sin4t is applied to the system.  Find the equation of motion if the surrounding medium offers a damping force numerically equally to 8 times the instantaneous velocity.