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## Homework Statement

A driven oscillator satisfies the equation

x'' + omega

^{2}=F0cos(omega(1+episilon)t]

where episilon is a positive constant. Show that the solution that satisfies the iniitial conditions x=0 and x'=0 when t=0 is

x= (F0*sin(.5episilon*omega * t) sin(omega(1+.5episilon)t)/(episilon(1+.5episilon)omega^2)

## Homework Equations

## The Attempt at a Solution

cos(omega*t)=cos omega(1+.5episilon)t-.5omega*t)

cos(omega(1+episilon)t)=cos(omega(1+.5episilon)t + .5omega*t)

let x=ce

^{iwpt}

x'= ciw

_{p}e

^{iwpt}

x''= -c*w

_{p}e

^{]iwpt}

c= F0/(-w

_{p}

^{2}+omega^2)

Therefore

x= (F0/(-w

_{p}

^{2}+omega^2))*ce

^{iwpt}

Am I heading in the right direction

Should I derived an equation for the complimentary solution?

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