# 3 pistons inside a tube

1. The problem statement, all variables and given/known data
The inside of horizontal and ##1m## long tube is divided by 3 moving pistons (no friction) with ##m=1kg## into 4 identical parts – each containing ##10g## of Helium at constant temperature ##T=300K##. Calculate the frequency of oscillation for each piston around the equilibrium position, if the only force responsible for any movements is due to the change of gas pressure.

2. Relevant equations

3. The attempt at a solution

Here is what I got and think is wrong:

##F=pS## obviously.

##p=\frac{m}{MV}RT##

##F=\frac{m}{Mx}RT##

Now for each piston separately:
first one:

##-\frac{mRT}{M}(\frac{1}{x_1}+\frac{1}{x_2-x_1})=m\ddot{x_1}##

second:

##\frac{mRT}{M}(\frac{1}{x_2-x_1}-\frac{1}{x_3-x_2})=m\ddot{x_2}##

third:

##\frac{mRT}{M}(\frac{1}{x_3-x_2}-\frac{1}{x_3})=m\ddot{x_3}##

Where ##x_{n}=x_{n0}+\varepsilon _n##.

Now even if this would be right, I have no idea how to continue.

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