## 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).

1. anonymous

is it displacement????

2. anonymous

Yes, displacement. Sorry.

3. anonymous

|dw:1345989153738:dw|

4. anonymous

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

5. anonymous

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

6. anonymous

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. anonymous

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. anonymous

That helped me a lot. Thank you!