What is the Potential Energy of a Spring Between Two Masses?

[rakshit1992]

A planar object comprises of two masses joined by a linear spring with relaxed length p. The horizontal and the vertical displacements of the two masses are measured relative to a fixed point of reference as shown in the figure. What would be the potential energy of the spring?

My initial guess for this problem are that the spring will have a horizontal PE=(1/2)*k*(z-x)^2 and a vertical PE=(1/2)*k*(w-y)^2.

But something tells me that there might be the possibility of the PE=(1/2)*k*(sqrt(z^2+w^2)-p)^2-(1/2)*k*(sqrt(x^2+y^2)-p)^2.

Please help

 

[TSny]

Forget the x and y coordinates for the moment. If the distance between the masses is d, how would you express the PE in terms of d and the relaxed length p?

 

[rakshit1992]

In that case, I would assume it to be (1/2)*K*(d-p)^2

 

[TSny]

In that case, I would assume it to be (1/2)*K*(d-p)^2

OK. Express this in terms of the given quantities.