Meriam, Kraige & Bolton — Kinetics of Particles: Problem 3_117

3/117 The 0.8-kg particle is attached to the system of two light rigid bars, all of which move in a vertical plane. The spring is compressed an amount \(b/2\) when \(\theta = 0\), and the length \(b = 0.30 \text{ m}\). The system is released from rest in a position slightly above that for \(\theta = 0\). (a) If the maximum value of \(\theta\) is observed to be \(50^\circ\), determine the spring constant \(k\). (b) For \(k = 400 \text{ N/m}\), determine the speed \(v\) of the particle when \(\theta = 25^\circ\). Also find the corresponding value of \(\dot{\theta}\).