A question about central-force movement

[sapz]

Homework Statement

Hi there! Could you please help me with this question? Am I doing it right?

A particle is moving under a force of the form F(r) = -Ar^3 (r-hat). The particle begins its movement at a distance r0 and velocity v0.

A. Find and draw the effective potential. Can the particle arrive at r=0?
B. Find the velocity v0 so that the particle will move in a circle.
C. What is the frequency of the small movements (w0) around that radius?

Homework Equations

The Attempt at a Solution

The attempt is attached as an image.

 

[haruspex]

To sketch the graph, determine the asymptotic behaviours as r tends to 0, infinity, and find any local maxima and minima. Can it reach r = 0?
In B, you made an algebraic error going from the first line to the second. This propagated into your work in C.
In C, you left out centripetal acceleration in the second equation.

 

[sapz]

Thanks!