The kinetic energy of a segment ?m of a vibrating string is given by (a) Find the

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The kinetic energy of a segment ?m of a vibrating string is given by

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(a) Find the total kinetic energy of the nth mode of vibration of a string of length L fixed at both ends.

(b) Give the maximum kinetic energy of the string.

(c) What is the wave function when the kinetic energy has its maximum value?

(d) Show that the maximum kinetic energy in the nth mode is proportional to n2An2.

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