Classical Mechanics (Kibble & Berkshire) · Problem 5.4

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

Physics — Mechanics · free-linear-oscillations

Problem

An overdamped harmonic oscillator satisfies the equation

\ddot{x} + 10\dot{x} + 16x = 0.

At time

t = 0

the particle is projected from the point

x = 1

towards the origin with speed

u

. Find

x

in the subsequent motion. Show that the particle will reach the origin at some later time

t

\frac{u-2}{u-8} = e^{6t}.

How large must

u

be so that the particle will pass through the origin?