Two identical masses (m) on a frictionless plane have a spring in between them. The spring has a length (L) when it is not compressed. The spring has been compressed between the two masses so it has a length Lo. The frictionless plane is at the bottom of a valley with the two inclined planes on either side of the masses. Both inclined planes have coefficients of kinetic friction of µk and angles of inclination of θ.
If the spring between the masses is released and allowed to expand, what is its spring constant if both masses make it a distance of D up each incline?
(find the spring constant k in terms of m, L, Lo, θ, µk, D and g)