All Problems

Mechanical Oscillations

Problem 4.45

A uniform rod of mass \(m=1.5\) kg suspended by two identical threads \(l=90 \mathrm{~cm}\) in length (Fig. 4.13) was turned through a small angle about the vertical axis passing through its middle point C. The threads deviated in the process through an angle \(\alpha=5.0^{\circ}\). Then the rod was released to start performing small oscillations. Find: (a) the oscillation period; (b) the rod's oscillation energy.

Reveal Answer
(a) \(T=2 \pi \sqrt{l / 3 g}=1.1 \mathrm{~s}\) (b) \(E=1 / 2 m g l \alpha^{2}=0.05 \mathrm{~J}\).