Introduction to Classical Mechanics · Problem 12.9

Relativity (Dynamics) — Morin

Physics — Mechanics · relativistic-force-momentum

Problem

A particle of mass

m

moves along the

x

axis under a force

F = -m\omega^2 x

. The amplitude is

b

. Show that the period is given by

T = \frac{4}{c} \int_0^b \frac{\gamma}{\sqrt{\gamma^2 - 1}}\, dx, \quad \text{where} \quad \gamma = 1 + \frac{\omega^2}{2c^2}(b^2 - x^2).