Waves and Oscillations - Continuous Media : Energy of a Vibrating String

A vibrating string possesses kinetic as well as potential energy. The kinetic energy is due to the velocity the element of the string has at that instant of time and the potential energy is the work done by the tension in extending the element. Finding the extension in length of a element of the string the potential and kinetic energy have been found using the first principle. The total energy of the string is the sum of the energies associated with all the normal modes of the string. The energy in each mode is found by finding the displacement for that mode. The total energy is found by summing the energy associated with each of its normal modes.

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