1. The problem statement, all variables and given/known data A bead of mass m is free to move on a stationary frictionless hoop of radius R. The hoop is in a horizontal plane (no need to take gravity into account) and it is located a distance d from a stationary wall. The bead is attached to the wall by a spring (constant k and natural length L). Find the frequency of small oscillations about the equilibrium points. -Just to clarify the problem further, if you draw a line perpendicular to the wall and passing through the diameter of the hoop the point where the line intersects the wall is where the other end of the spring is attached to. The other end is of course attached to the bead. 2. Relevant equations the Lagrangian, lagranges equations, kinetic and potential energy of the system. small angle sine and cosine approx's 3. The attempt at a solution I obtained a solution that makes perfect physical sense, but I did not include the natural length of the spring in my initial solution. my question is does the natural length affect the solution to this problem? Again the first time I went through this I thought i could simply ignore it because it was a constant, thinking the lagrange equations would make it disappear. Working through it again I realized this was probably not the case, tried solving the equations and ended up with a solution that was a lot uglier.