A string of mass `m` is fixed at both ends. The fundamental tone oscillations are excited with circular frequency `omega` and maximum displacement amplitude `a_(max)` . Find `:`
`(a)` the maximum kinetic energy of the string,
`(b)` the mean kinetic energy of the string averaged over one oscillation period.

Explanation

To solve the problem, we need to find the maximum kinetic energy and the mean kinetic energy of a string fixed at both ends, vibrating in its fundamental mode. Let's break this down step by step.

### Step 1: Understand the system
We have a string of mass \( m \) fixed at both ends, oscillating in its fundamental mode with circular frequency \( \omega \) and maximum displacement amplitude \( a_{\text{max}} \).

### Step 2: Determine the mass per unit length
The mass per unit length \( \mu \) of the string is given by:
\[
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