A metallic rod of length 1m is rigidly clamped at its mid point. Longirudinal stationary wave are setup in the rod in such a way that there are two nodes on either side of the midpoint. The amplitude of an antinode is `2 xx 10^(-6) m`. Write the equation of motion of a point 2 cm from the midpoint and those of the constituent waves in the rod, (Young,s modulus of the material of the rod `= 2 xx 10^(11) Nm^(-2)` , density `= 8000 kg-m^(-3)`). Both ends are free.

Explanation

To solve the problem step by step, we will derive the equations of motion for a point 2 cm from the midpoint of the metallic rod, as well as the equations for the constituent waves.

### Step 1: Understand the setup
The metallic rod is 1 m long and clamped at its midpoint. This means that the midpoint is a node, and there are two nodes at the ends of the rod. The wave setup creates longitudinal stationary waves.

### Step 2: Identify the given parameters
- Length of the rod (L) = 1 m
- Amplitude of the antinode (A) = \(2 \times 10^{-6}\) m
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