A mass that weighs 8 lb stretches a spring 4 in. The mass is attached to a dashpot mechanism that has a damping constant of 0.25lb-sec/ft. The system is acted on by an external force of 6sin 8t lb. The mass is pulled down 3 in and then released. 1. Determine the spring constant 2. Write the differential equation governing the motion of the mass. Also write the initial conditions. 3. Determine the transient motion of the damped mass-spring system. 4. Determine the steady periodic oscillations of the damped mass-spring system.