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Richardbryant
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Homework Statement
An undamped harmonic oscillator (b=0) is subject to an applied force Focos(wt). Show that if w=wo, there is no steady- state solution. Find a particular solution by starting with a solution for w=wo+#, and passing to the limit #->0, it will blow up. Try starting with a solution which fits the initial condition xo=0, so that i cannot blow up at t=0.
Homework Equations
The Attempt at a Solution
d^2x/dt^2+(wo^2)x=Fo cos(w+#)t/m
d^2y/dt^2+(wo^2)y=Fo sin(w+#)t/m
d^2z/dt^2+(wo^2)z=Foe^i(w+#)t/m (1)
Let Z=Ce^i(wo+#)t, plug in (1)
C=Fo/,[wo^2-(w+#)^2]
thus X= Fo cos(w+#)t/m[wo^2-(w+#)^2]
Xtr (trasient term )=Acos(wot-$) $= phase difference
After a couple of steps the final solution will blow up when limit #->0[/B]