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seidi.yamauti

  • 2 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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  1. damrinder
    • 2 years ago
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    is it displacement????

  2. seidi.yamauti
    • 2 years ago
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    Yes, displacement. Sorry.

  3. henpen
    • 2 years ago
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    |dw:1345989153738:dw|

  4. henpen
    • 2 years ago
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    \[F_{total}=ma=m\frac{d^2x}{dt^2}=-kx+F_0\sin(wt)\]

  5. henpen
    • 2 years ago
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    \[\frac{d^2x}{dt^2}-kx/m=F_0\sin(wt)/m\]

  6. henpen
    • 2 years ago
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    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

  7. henpen
    • 2 years ago
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    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

  8. seidi.yamauti
    • 2 years ago
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    That helped me a lot. Thank you!

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