An ant with mass `m` is standing peacefully on top of a horizontal, stretched rope. The rope has mass per unit length `mu` and is under tension `F`. Without warning, a student starts a sinusoidal transverse wave of wavelength `lambda` propagating along the rope. the motion of the rope is in a verticle plane. what minimum wave amplitude (in mm) will make the ant feel weightless momentarily? Assume that `m` is so small that the presence of the ant has no effect on the propagation of the wave.
[Given: `lambda=0.5 m,mu=0.1 kg//m,F=3.125 N,take g=pi^(2)`]

Explanation

To solve the problem, we need to find the minimum wave amplitude that will make the ant feel weightless momentarily. Let's break down the solution step by step.

### Step 1: Understanding the Condition for Weightlessness
For the ant to feel weightless, the upward acceleration of the wave must equal the acceleration due to gravity. This means that the maximum acceleration of the wave must be equal to \( g \).

### Step 2: Maximum Acceleration of the Wave
The maximum acceleration \( a_{max} \) of a wave on a rope is given by the formula:
\[
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