Potential energy of a vibrating string?

[torehan]

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.

 

[Redbelly98]

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.