Chapter 14, Problem 14.87P

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 constant k is attached to the lower end of the rod, with the other end of the spring attached to a rigid support. If the rod is displaced by a small angle Θ from the vertical (Fig. P14.87) and released, show that it moves in angular SHM and calculate the period. (Hint: Assume that the angle Θ is small enough for the approximations sin Θ ≈ Θ and cos Θ ≈ 1 to be valid. The motion is simple harmonic if d²θ/dt² = −ω²θ, and the period is then T = 2π/ω.)

Figure P14.87