The bar of weight w is pinned at its center O and connected to a torsional spring. The spring has a stiffness k, so that the torque developed is M = kθ. If the bar is released from rest when it is vertical at θ = 90°, determine its angular velocity at the instant θ = θ₁.

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Given: W = 10 lb k = 5 lb. ft rad a = 1 ft 8 = 32.2 01 2 S = 45 deg