Classical Mechanics (Kibble & Berkshire) · Problem 5.14

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

Physics — Mechanics · nonlinear-oscillations-coulomb-friction

Problem

Coulomb friction The displacement

x

of a spring mounted mass under the action of Coulomb friction satisfies the equation

\ddot{x} + \Omega^2 x = \begin{cases} -F_0 & \dot{x} > 0 \\ F_0 & \dot{x} < 0 \end{cases}

where

\Omega

and

F_0

are positive constants. If

|x| > F_0/\Omega^2

when

\dot{x} = 0

, then the motion continues; if

|x| \leq F_0/\Omega^2

when

\dot{x} = 0

, then the motion ceases. Initially the body is released from rest with

x = 9F_0/2\Omega^2

. Find where it finally comes to rest. How long was the body in motion?