## seidi.yamauti Group Title 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

1. damrinder Group Title

is it displacement????

2. seidi.yamauti Group Title

Yes, displacement. Sorry.

3. henpen Group Title

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4. henpen Group Title

$F_{total}=ma=m\frac{d^2x}{dt^2}=-kx+F_0\sin(wt)$

5. henpen Group Title

$\frac{d^2x}{dt^2}-kx/m=F_0\sin(wt)/m$

6. henpen Group Title

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 Group Title

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 Group Title

That helped me a lot. Thank you!