Vol 1 - L D Landau, E.M. Lifshitz - Mechanics · Problem 22.1

Small Oscillations

Physics — Landau & Lifshitz · forced-oscillations

Problem

Determine the forced oscillations of a system under a force

F(t)

of the following forms, if at time

t = 0

the system is at rest in equilibrium (

x = \dot{x} = 0

): (a)

F = F_0

, a constant, (b)

F = at

, (c)

F = F_0 \exp(-\alpha t)

, (d)

F = F_0 \exp(-\alpha t) \cos \beta t