Introduction to Classical Mechanics · Problem 4.7

Conservation of energy and momentum — Morin

Physics — Mechanics · driven-harmonic-motion

Problem

A particle of mass

m

is subject to a force

F(t) = ma_0 e^{-bt}

. The initial position and speed are both zero. Find

x(t)

. (This problem was already given as Problem 3.9, but solve it here by guessing an exponential function, in the spirit of Section 4.4.)