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## Homework Statement

I want to find an expression for the eigenfrequencies of a vertical spring-mass-spring-mass system by using the potential energy

**V**and kinetic energy

**T**in matrixform. Both springs have the springconstants

**k,**and both masses are

**m**. The springs unstretched length are

**l**.

I have chosen

**y_1**to represent the displacement from equilibrium of mass 1 (upper mass) and

**y_2**the displacement for equilibrium of mass 2 (lower mass). I have also chosen the positive y-direction to be towards the ceiling.

My skills in mechanics is a bit rusty and i need help to find an expression for the potential energy

**V**, i think i can do the rest from there.

## The Attempt at a Solution

My attempt at writing an expression for

**V**is

**V = mg(y_1 + y_2) + k/2(y_1)^2 + k/2(y_2 - y_1)^2**

The

**y_2 - y_1**is there because when the upper mass is displaced downwards this will compress the lower string.

I do realise i need to have something about the equlibrium for the system in

**V,**but im not sure how.

Thanks for any help!

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