All Problems

Mechanical Oscillations

Problem 4.60

Find the period of small torsional oscillations of a system consisting of two discs slipped on a thin rod with torsional coefficient \(k\). The moments of inertia of the discs relative to the rod's axis are equal to \(I_{1}\) and \(I_{2}\).

Reveal Answer
T=2πVI/k, where I=I1I2/(I1+I2)T=2 \pi V \overline{I^{\prime} / k}, \text { where } I^{\prime}=I_{1} I_{2} /\left(I_{1}+I_{2}\right)