A mass weighing 4 lb stretches a spring 2 in. Suppose that the mass is given an additional 6-in displacement in the positive direction and then released. The mass is in a medium that exerts a viscous resistance of 6 lb when the mass has a velocity of 3 ft/s. Under the assumptions discussed in this section, formulate the initial value problem that governs the motion of the mass.

Explanation:

The standard form of the 2nd order differential equation governing the motion of mass-spring system is given by

Where m is the mass, ζ is the damping constant, and k is the spring constant.

The spring constant k can be found by

The damping constant can be found by

Finally, the mass m can be found by

Where g is approximately 32 ft/s²

Therefore, the required differential equation is

The initial position is

The initial velocity is