Two springs from the ceiling attached to one mass, least energy principle

[charliepebs]

1.
Suppose have a ball connected to a spring on each end – one with constant k, and the other with constant K. And suppose the springs are attached to the ceiling a distance d apart. Use energy minimization methods to determine the (x,y) coordinates of the mass in equilibrium – taking the origin of the coordinate system to be the point where spring K is attached to the ceiling.





2. φ=1/2k(stretch)^2
least energy principle: ∂φ/∂r=0

3. Not a lot of specifics given in this problem as far as initial conditions, stretched upon attachment, etc., not sure whether to use polar or Cartesian. I know I need a constraint, probably that since the springs are connected to the same point, the vector of one plus the vector of the other must equal the distance between them. Just not sure how to handle the fact that length of both springs and the angle they both make with the ceiling is changing simultaneously.

 

[rude man]

Length of each spring? Obviously matters. Or can the answer be given in terms of the lengths L1 and L2 so that the mass m is situated at p(x,y), x= x(m,L1, L2, d) and y = y(m,L1,L2,d)?