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**1. Homework Statement**

The kinetic energy of a segment of length [tex] \Delta x [/tex] and mass [tex] \Delta m [/tex] of a vibrating string is given by [tex] \Delta K = \frac{1}{2} \Delta m (\frac{\partial y}{\partial t})^2 = \frac{1}{2} \mu (\frac{\partial y}{\partial t})^2 \Delta x [/tex], where [tex] \mu = \frac{\Delta m}{\Delta x} [/tex].

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 [tex] n^2 A_n^2 [/tex].

**2. Homework Equations**

Pretty much given.

**3. The Attempt at a Solution**

I have tried numerous times to get a start on this problem but I can't seem to figure it out. Neither can my older brother or other peers .