A magnet free to vibrate about vertical axis passing through its CM is first kept in a non- magnetic hook along BH.
On deflecting it slightly by an amount θ, it experiences a restoring torque due to horizontal component of earth’s field BH
τ = M BH sinθ
≈M BH θ [As sinθ ≈ θ, for small angle deflection.
Due to inertia of the magnet it start oscillating simple harmonically. We know from the theory angular SHM that linear frequency, angular frequency & time period of oscillations is,
Thus for this situation we have
Here, I = MI of the magnet
For two dissimilar magnets using
Here Ts = time period for the sum position & Td = time period for the difference position.