Homework Help: Pendulum involving conservative energy

1. Apr 11, 2005

insertnamehere

Hey! I need help with this question:
A ball having mass m is connected by a strong string of length L to a pivot point and held in place in a vertical position. A wind exerting constant force of magnitude F is blowing from left to right. If the ball is released from rest, show that the maximum height H reached by the ball, as measured from its initial height, is H= (2L)/(1+(mg/F)^2) Check that the above result is valid both for cases when 0<H,L and for L<H<2L.
So far, I know that I'm supposed to use FLsin(theta)=mgH
and integrate it -> W=(integral)FLcos(theta)d(theta)
But I have no idea at all where to go from here!! Please, i really need help now!! I don't have much time left for this!!

2. Apr 12, 2005

Andrew Mason

The solution to the pendulum motion without the wind is:

$$\theta = \theta_0,sin(\omega t)$$ where $\omega = \sqrt{g/L}$

When you add the wind, the energy added on the forward cycle is lost on the reverse cycle so this is equivalent to a new vibration about a different equilibrium position in which the new g' is determined from the vector sum of mg and F.

$$g' = \sqrt{g^2 +(F/m)^2}$$ and

[tex]\theta_0' [/itex] is the angle that the vector sum of F and mg makes to the vertical. Try working out H from that.

AM