Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_211

2/211 At time \( t = 0 \), the 1.8-lb particle \( P \) is given an initial velocity \( v_0 = 1 \text{ ft/sec} \) at the position \( \theta = 0 \) and subsequently slides along the circular path of radius \( r = 1.5 \text{ ft} \). Because of the viscous fluid and the effect of gravitational acceleration, the tangential acceleration is \( a_t = g \cos \theta - \frac{k}{m}v \), where the constant \( k = 0.2 \text{ lb-sec/ft} \) is a drag parameter. Determine and plot both \( \theta \) and \( \dot{\theta} \) as functions of the time \( t \) over the range \( 0 \le t \le 5 \text{ sec} \). Determine the maximum values of \( \theta \) and \( \dot{\theta} \) and the corresponding values of \( t \). Also determine the first time at which \( \theta = 90^\circ \).