All Problems

Mechanical Oscillations

Problem 4.45

A uniform rod of mass m=1.5m=1.5 kg suspended by two identical threads l=90 cml=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 α=5.0\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=2πl/3g=1.1 sT=2 \pi \sqrt{l / 3 g}=1.1 \mathrm{~s} (b) E=1/2mglα2=0.05 JE=1 / 2 m g l \alpha^{2}=0.05 \mathrm{~J}.