The pointer on a metronome supports slider A of weight W, which is positioned at a fixed distance a from the pivot O of the pointer. When the pointer is displaced, a torsional spring at O exerts a restoring torque on the pointer having a magnitude M = kθ where θ represents the angle of displacement from the vertical. Determine the natural period of vibration when the pointer is displaced a small amount and released. Neglect the mass of the pointer.

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Given: W = 0.4 lb k = 1.2 lb ft rad a = 0.25 ft 8 = 32.2 ft 2 A 0