1. The problem statement, all variables and given/known data Consider a particle moving back and forth on a frictionless parabolic bowl, y = ax2, where a = 1.460 m-1 If the particle is released from rest at the point on the bowl at b = 0.43 m, find the period of the oscillations. I have an equation for velocity(as a function of x). What i was thinking is that i could integrate this from -b to +b, and call this value 'v(x)*d', (it having units of m2/s. since v=d/t, v(x)*d=d2/t. thus t=d2/'v(x)*d'. making the period, T=2*(d2/'v(x)*d'), where d is the arc length of y(x), from -b to +b. I realize this may be the least elegant and very possibly "physically incorrect", but it actually gave me a period very close to that obtained by the 'small angle approximation' (however, incorrect) Can anybody comment on this method?