- 2

- 0

**1. Homework Statement**

I'd really appreciate it if someone could point me in the right direction in terms of equations to use for this problem:

Bar magnet suspended at either end by 2 pieces of string which are attached vertically above the magnet to a stationary metal rod (so that the bar magnet oscillates rotationally), underneath the magnet I placed a sheet of aluminium, so when i rotated the magnet and released it, the oscillations were damped by the eddy current induced in the sheet of aluminium below it. I understand that this is because the eddy current induced in the aluminium has its own magnetic field, and a force acts between this field and the magnetic field of the bar magnet.

**2. Homework Equations**

I have already derived equations for undamped motion of the system, and can find the starting energy of the system by either integrating torque with respect to x (x being original angle displace) or by using E=0.5Iw^2 (w=rotational velocity.) The equations for torque (T), acceleration (a) and velocity (w)in terms of x are :

T=-0.1sinx(0.5+0.5cosx)^0.5

a=T/I (I=moment of inertia=1/375 in my set up)

w^2=100(0.5+0.5cosx)^1.5 - 25root2 (25root2 is due to starting angle of pi/2)

I dont think the equations affect the solution to the magnetic problem, I just thought id add them for anyone who is interested.

**3. The Attempt at a Solution**

I have found the equations for undamped motion, and understand the principle of the dampening, I considered trying to use faraday's law saying the aluminium sheet could be treated as a one turn coil? but my friend said that was wrong. Presumably the solution will be only solvable if i have equations of motion in terms of time rather than angle displaced, ill work on that.

In terms of explanations- my maths understanding extends to A level Further Pure.

Thanks.