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A certain of a perfect gas is enclosed i...

A certain of a perfect gas is enclosed in a cylinder of volume `V_(0)` fitted with a smooth heavy piostion of mass m and area a. The piston is displaced through a small distance downwards so as to compress the gas isother mally , and then it is left free to go show that it performs SHM and also find its period . Take the atmospheric pressure as `P_(atom)`.

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To solve the problem, we will follow these steps: ### Step 1: Understand the system and initial conditions We have a cylinder with a piston that contains a perfect gas. The piston is initially at rest, and the system is in equilibrium with atmospheric pressure acting on one side and the gas pressure on the other side. The initial pressure of the gas is denoted as \( P \) and the atmospheric pressure as \( P_{atm} \). ### Step 2: Establish the equilibrium condition At the mean position (equilibrium position), the forces acting on the piston are balanced. Therefore, we can write the equation: \[ ...
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