The figure shows a 170 g uniform rod pivoted at one end.The other end is attached to a horizontal spring. The spring isneither stretched nor compressed when the rod hangs straightdown. What is the rod's oscillation period? You can assume that therod's angle from vertical is always small. The figure shows a 170 g uniform rod pivoted at one end.The other end is attached to a horizontal spring. The spring isneither stretched nor compressed when the rod hangs straightdown. What is the rod's oscillation period? You can assume that therod's angle from vertical is always small.
Explanation / Answer
M L d2 / dt2 = - M g sin equation ofmotion of simple pendulum P = 2 (L /g) solution for simplependulum I d2 = - M g L sin /2 equation of motion of compoundpendulum where torque equals angular acceleration P = 2 (2 I / M gL) where I = moment of inertiaand L / 2 is distance to center of mass If we use L k sin as the restoring torque due tothe spring I d2 = - M g L sin / 2 - Lk sin then P = 2 (I / (M g L + L k)) Use I = M L2 / 3 andsolve