Potential energy of a vibrating string?

AI Thread Summary
To calculate the potential energy of a vibrating string, one approach is to consider the work done by the string during deformation. The maximum kinetic energy can be determined for a specific amplitude of vibration and equated to the potential energy at maximum amplitude. The process involves calculating the transverse velocity of the string at zero displacement and integrating the kinetic energy formula across the string's length. This method relies on the principle of conservation of energy, linking kinetic and potential energy. Understanding these relationships is crucial for accurately determining the potential energy in vibrating strings.
torehan
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How can I calculate potential enegry?

I have a interpretation about it, we should use the work that the string does. But there is deformation on dicplacement of the string.

waiting for the any ideas.
 
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I would try calculating the maximum kinetic energy for a given amplitude of string vibration, then equate that with the potential energy when the string is at it's maximum amplitude of vibration.

I.e., for a given amplitude, what is the velocity of the string at zero displacement? Then integrate (1/2)(M/L)v^2 over the entire length to get total kinetic energy. Note, "v" is the transverse velocity, not the wave velocity.

By conservation of energy, this result equals the potential energy when the string is at it's maximum displacement.
 

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