Introduction to Classical Mechanics · Problem 4.25

Conservation of energy and momentum — Morin

Physics — Mechanics · damped-harmonic-motion

Problem

In the strong damping (

\gamma \gg \omega

) case discussed in the remark in the overdamping subsection, we saw that

x(t) \propto e^{-\omega^2 t/2\gamma}

for large

t

. Using the definitions of

\omega

and

\gamma

, this can be written as

x(t) \propto e^{-kt/b}

, where

b

is the coefficient of the damping force. By looking at the forces on the mass, explain why this makes sense.