A slender, uniform, metal rod

A slender, uniform, metal rod with mass M is pivoted with out 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 o end of the spring attached to a rigid support. If the rod is displaced by a small angle e from the vertical (Fig. 13.40) and released, show iliat it moves in angular SHM and calculate the period. (Hint: Assume iliat 1he angle e is small enough for the approximations sin e = e and case = 1 to be valid. The motion is simple harmonic if d’fJ/dt2 = -20 and the period is ten T = 2w/)

Solution:

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