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!