# 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.

http://ift.tt/Uj4fIz

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