 #1
happyparticle
 373
 19
 Homework Statement:
 equation of motion
 Relevant Equations:

F = ma
##\ddot{\theta} + \frac{k}{m} x = 0##
Hi,
I have a particle on a parabolic surface $$y = Ax^2$$ and I have to show that the frequency is $$\omega = \sqrt{2Ag}$$
I don't know how to deal with a parabola. I don't think I can use the polar coordinates like a circle.
I don't see how to start this problem and in which coordinates system.
For a circle I can use the polar coordinates and then use ##F = ma => mg sin \theta = mR\ddot{\omega}##
I have to get the equation of motion $$\ddot{\theta} + 2Ag \theta = 0$$
thus, ##2Ag = \omega^2##
I have a particle on a parabolic surface $$y = Ax^2$$ and I have to show that the frequency is $$\omega = \sqrt{2Ag}$$
I don't know how to deal with a parabola. I don't think I can use the polar coordinates like a circle.
I don't see how to start this problem and in which coordinates system.
For a circle I can use the polar coordinates and then use ##F = ma => mg sin \theta = mR\ddot{\omega}##
I have to get the equation of motion $$\ddot{\theta} + 2Ag \theta = 0$$
thus, ##2Ag = \omega^2##