# Driven Oscillator

*Michael Fowler* (*closely following* *Landau para 22*)

Consider a one-dimensional simple harmonic oscillator with a variable external force acting, so the equation of motion is

which would come from the Lagrangian

(Landau "derives" this as the leading order non-constant term in a time-dependent external potential.)

The general solution of the differential equation is , where , the solution of the homogeneous equation, and is some particular integral of the inhomogeneous equation.

An important case is that of a periodic driving force A trial solution
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