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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).
 one year ago
 one year ago
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).
 one year ago
 one year ago

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damrinderBest ResponseYou've already chosen the best response.0
is it displacement????
 one year ago

seidi.yamautiBest ResponseYou've already chosen the best response.0
Yes, displacement. Sorry.
 one year ago

henpenBest ResponseYou've already chosen the best response.1
\[F_{total}=ma=m\frac{d^2x}{dt^2}=kx+F_0\sin(wt)\]
 one year ago

henpenBest ResponseYou've already chosen the best response.1
\[\frac{d^2x}{dt^2}kx/m=F_0\sin(wt)/m\]
 one year ago

henpenBest ResponseYou've already chosen the best response.1
From SHM,\[k=w_0^2m\] rewrite sin(wt) as cos(wt90), 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
 one year ago

henpenBest ResponseYou've already chosen the best response.1
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
 one year ago

seidi.yamautiBest ResponseYou've already chosen the best response.0
That helped me a lot. Thank you!
 one year ago
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