(a) Two springs are attached in series as shown in Figure 5.R.1. If the mass of each spring is ignored, show that the effective spring constant k of the system is defined by 1/k = 1/k₁ + 1/k₂.

(b) A mass weighing W pounds stretches a spring foot and stretches a different spring foot. The two springs are attached, and the mass is then attached to the double spring as shown in Figure 5.R.1. Assume that the motion is free and that there is no damping force present. Determine the equation of motion if the mass is initially released at a point 1 foot below the equilibrium position with a downward velocity of 2/3 ft/s.

(c) Show that the maximum speed of the mass is 2/3√3g + 1.

FIGURE 5.R.1