- #1

happyparticle

- 441

- 20

- 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##