Question

14.87 .. CALC A slender, uniform, metal rod with mass M is pivoted without friction about an axis through its midpoint and perpendicular to the rod. A horizontal spring with force con- stant k is attached to the lower end of the rod, with the other end Figure P14.87 of the spring attached to a rigid support. If the rod is displaced by a small angle from the vertical (Fig. P14.87) and released, show that it moves in angular SHM and calculate the period. (Hint: Assume that the angle is small enough for the approximations [ sin Ꮎ = Ꮎ and cos Ꮎ = 1 to be valid. The motion is simple har- monic if d-0/dt = -0-0, and the period is then T = 27/0.)