Classical Mechanics (Kibble & Berkshire) · Problem 5.3

Energy conservation — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · free-linear-oscillations

Problem

A particle of mass

m

moves along the

x

-axis and is acted upon by the restoring force

-m(n^2 + k^2)x

and the resistance force

-2mk\dot{x}

, where

n

k

are positive constants. If the particle is released from rest at

x = a

, show that, in the subsequent motion,

x = \frac{a}{n}e^{-kt}(n\cos nt + k\sin nt).

Find how far the particle travels before it next comes to rest.