# Central Force

I have a problem for this question, please help me

A particle of mass m is moving in an attractive inverse cubed force given by

F = -K/r^3, where K>0

a) Find V(r) and plot V(r) versus r.
b) Discuss the motion qualitatively by the method of effective potential.
C) Find E and L when the particle is moving in a circular orbit.
d) Find the time period of the orbit.
e) If the orbit is perturbed slightly, what will be the period of small oscillations?

## Answers and Replies

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Tide
Science Advisor
Homework Helper
What, exactly, have you done so far?

I don't know a shape of V(r) versus r

<i>I don't know a shape of V(r) versus r</i>

V is potential energy? Then V(r) is the integral of the force with respect to displacement.

Edit: make that the negative integral of the force etc.

Last edited:
I find V(r) = -k/2r^2 + L^2/2mr^2
a part of r^2 of two terms are equal. Which total graph of V(r)

HallsofIvy
Science Advisor
Homework Helper
I could interpret V(r) as velocity or potential energy. Also I have no idea what "E"and "L" are. Please be sure you define all terms.