All Problems

Mechanical Oscillations

Problem 4.44

Find the frequency of small oscillations of a thin uniform vertical rod of mass \(m\) and length \(l\) hinged at the point \(O\) (Fig. 4.12 ). The combined stiffness of the springs is equal to \(x .\) The mass of the springs is negligible.

Reveal Answer
ω=3g2l(1+2xlmg)\omega=\sqrt{\frac{3 g}{2 l}\left(1+\frac{2 x l}{m g}\right)}