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Vibration magnetometer is used for comparison of magnetic moments and magnetic fields. This machine operates on the rule, that whenever a freely open magnet in a uniform magnetic field, is divided from its equilibrium state, it starts vibrating about the mean state.
Time period of oscillation of experimental bar magnet (magnetic moment M) in earth's magnetic field is given by the formula. 
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Where, I= moment of inertia of short bar magnet = wL2/12(w = mass of bar magnet)
(3) Use of vibration magnetometer
(i) Calculation of magnetic moment of a magnet :
The experimental (given) magnet is put into vibration magnetometer and it's time period T is determined. Now 
(ii) Comparison of horizontal components of earth's magnetic field at two places.
Since I and M the magnet are constant,
So 
(iii) Comparison of magnetic moment of two magnets of same size and mass.
Here I and BH are constants.
So 
(iv) Difference of magnetic moments of two magnets of unequal sizes and masses (by sum and difference method) :
In this method both the magnets vibrate simultaneously in two following position.
Sum position
Two magnets are stable such that their magnetic moments are additive
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Net magnetic moment Ms = M1 + M2
Net moment of inertia Is = I1 + I2
Time period of oscillation of that pair in earth's magnetic field (BH)
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.....(i)
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