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seidi.yamauti
An undamped oscillator of mass m and natural frequency Wo moves under the action of an external force F=Fo sin(wt). Starting from the equilibrium position with initial velocity zero. Find the deslocament x(t).
is it displacement????
Yes, displacement. Sorry.
\[F_{total}=ma=m\frac{d^2x}{dt^2}=-kx+F_0\sin(wt)\]
\[\frac{d^2x}{dt^2}-kx/m=F_0\sin(wt)/m\]
From SHM,\[k=w_0^2m\] rewrite sin(wt) as cos(wt-90), x will tend to take the form\[Acos(wt)\]. You just need to find A. You could either use normal DE or assume x is a complex number and turn F_0sinwt into F_0e^iwt
To use the normal method:\[Aw^2\sin(wt)-Amw_0\sin(wt)/m=F_0\sin(wt)\] Rearrange to find A. I assumed that x=Asin(wt) for convenience
That helped me a lot. Thank you!