Question

The angular velocity and amplitude of simple pendulum is θ and r respectively. At a displacement x from the mean position, if its kinetic energy is T and potential energy is V, find the ratio of T to V.

Answer 1

Kinetic energy, T = \(\frac{1}{2}mv^2= \frac{1}{2}mω^2(r^2\,-\,x^2);\)

Potential energy, V = \(\frac{1}{2}mω^2x^2\)

So, \(\frac{T}{V}= \frac{r^2-x^2}{x^2}\)