Classical Dynamics of Particles and Systems · Problem 2-13

Oscillations — Marion & Thornton

Physics — Mechanics · particle-retarding-force-maximum-distance

Problem

A particle moves in a medium under the influence of a retarding force equal to

mk(v^3 + a^2v)

, where

k

and

a

are constants. Show that for any value of the initial speed the particle will never move a distance greater than

\pi/2ka

and that the particle comes to rest only for

t \to \infty