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Classical Mechanics Level 5

A thin conducting wire of length \(L\), resistance \(R\) made of a non-magnetic material of uniform linear mass density \(\mu\) is fitted between two metal walls which are connected to each other via a thick metal strip. A tension \(T\) is maintained in the wire.

The wire is made to vibrate in its fundamental mode. At an instant when the wire is at one of the extreme positions, a uniform magnetic field of magnitude \(B_0\) perpendicular to the plane of vibration is turned on in the area between the walls. This magnetic field damps the vibration of the wire.

Find the time taken(in seconds) for the amplitude of vibration to become half its initial value.

Details and Assumptions:

  1. \(L=1 m\), \(\mu=0.25Kgm^{-1}\), \(T=100N\), \(R=10\Omega\), \(B_0=0.1\pi T\)

  2. Assume tension to be uniform throughout the string

  3. Assume that the wave oscillates in fundamental mode throughout the experiment.

You may use any computer resource to solve the problem. If you genuinely feel that this is incorrect, feel free to report.


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