1. The problem statement, all variables and given/known data Consider a solid sphere of radius r to be placed at the bottom of a spherical bowl radius R, after the ball is given a push it oscillates about the bottom. By using the Lagrangian approach find the period of oscillation. 2. Relevant equations 3. The attempt at a solution Ok so this is as far as i get, not sure if what im doing is correct: General coords (∅,x,y) T = 1/2*m*(xdot2+ydot2) + 1/2*I*∅dot2 T = 1/2*m*xdot2+1/2*m*ydot2+(mr2∅2)/5 (Since Inertia of Solid Sphere is = 2/5*m*r2) V = mgy L = 1/2*m*xdot2+1/2*m*ydot2+(mr2∅2)/5 - mgy ∂L/∂∅dot = 2/5*m*r2*∅dot ∂L/∂∅ = 0 ∂L/∂xdot = m*xdot ∂L/∂x = 0 ∂L/∂ydot = m*ydot ∂L/∂y = -mg d(2/5*m*r2*∅dot)/dt = 0 d(m*xdot)/dt = 0 d(m*ydot)/dt = -mg Up to here im not sure whether i've been doing the right thing, and also, not quite sure how this helps me find the period of oscillation? EDIT: Sigh, I know my equations of motion are wrong because i should be getting something similar to the DE for an SHO. Could really use some help.