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anonymous
 4 years 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).
anonymous
 4 years 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).

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0is it displacement????

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Yes, displacement. Sorry.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1345989153738:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[F_{total}=ma=m\frac{d^2x}{dt^2}=kx+F_0\sin(wt)\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\frac{d^2x}{dt^2}kx/m=F_0\sin(wt)/m\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0From 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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0To 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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0That helped me a lot. Thank you!
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