# Parabolic Bowl

jderm

## Homework Statement

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?

## Answers and Replies

jderm
i guess the crux of my argument is whether the area under the v(x) curve can be used in this manner, comments?

RoyalCat
The acceleration and velocity are not at all constant, so the method is, mathematically speaking, completely wrong.