A mass m is attached to the end of a spring whose constant is k. After the

Question:

A mass m is attached to the end of a spring whose constant is k. After the mass reaches equilibrium, its support begins to oscillate vertically about a horizontal line L according to a formula h(t). The value of h represents the distance in feet measured from L. See Figure 5.1.21.

(a) Determine the differential equation of motion if the entire system moves through a medium offering a damping force that is numerically equal to β(dx/dt).

(b) Solve the differential equation in part (a) if the spring is stretched 4 feet by a mass weighing 16 pounds and β = 2, h(t) = 5 cos t, x(0) = x'(0) = 0.

Figure 5.1.21.

support L ww