Stable and Unstable Equilibriums in a Spring-Mass System on a Loop

[yxgao]

Imagine drawing the following figure: draw a circle and a diameter. They are made of massless wire. There's a spring attached a distance d from the center of the hoop on the diameter, and a mass on the other end of the spring.

Using physical intuition, where would the two stable equibriums and two unstable equilibriums be?



Note:
natural length of spring is 0
the hoops rolls without slipping
straight wire is massless
yes, the mass can slide both ways
each end of the wire is connected to the loop

 

[ee7klt]

is the pivot point moveable? (i.e. does d=d(t) or does d=const)

 

[yxgao]

No, the pivot point of the spring is fixed.