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Benzoate
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Homework Statement
A driven oscillator satisfies the equation
x'' + omega2=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=ceiwpt
x'= ciwpeiwpt
x''= -c*wpe]iwpt
c= F0/(-wp2+omega^2)
Therefore
x= (F0/(-wp2+omega^2))*ceiwpt
Am I heading in the right direction
Should I derived an equation for the complimentary solution?
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