Question

Prove that under certain conditions a

magnet vibrating in uniform magnetic

field performs angular S.H.M.

​

Answer 1

Follows are the description of the proving:

Explanation:

$\to \bold {\tau = m \times B}$

The above-given equation shows the frequency of this torque. It is the torque restoration because $\Theta$ seems to be the angle between both the saturation magnetization direction (m) as well as the magnetic field path B.

It may claim that, in balance,  

$\to I \frac{d^2 \theta}{d t}\cong - m B \sin \theta$

Its minus value throughout the expression square wave above allows everyone to conclude also that torque which recovers there works throughout the reverse way from the torque, that deflects. It can also approximate $\sin \theta = \theta$ which means the radians because the approximation is quite small.

$\to I \frac{d^2 \theta}{d t}\cong - m B \theta \\\\\to \frac{d^2 \theta}{d t}\cong - \frac{m B \theta}{I}$

This equation portrays a basic harmonic motion and the angular frequency can be calculated as,  

$\to \omega \cong - \frac{m B \theta}{I}$

And the time period can therefore be defined as:

$\boxed{\boxed{\bold{T = 2 \pi \sqrt{\frac{I}{mB}}}}}$

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