Classical Dynamics of Particles and Systems · Problem 3-31

Nonlinear Oscillations and Chaos — Marion & Thornton

Physics — Mechanics · step-function-response

Problem

A damped linear oscillator, originally at rest in its equilibrium position, is subjected to a forcing function given by

\frac{F(t)}{m} = \begin{cases} 0, & t < 0 \\ a \times (t/\tau), & 0 < t < \tau \\ a, & t > \tau \end{cases}

Find the response function. Allow

\tau \to 0

and show that the solution becomes that for a step function.