Question

the motion of a particle of mass m in the potential field V(r) = kr²/2 then the effective potential is
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Answer 1

A particle of mass m moves under the action of a central force whose potential is given by V(r)=Kr

3

,(K>0)

(i) For what energy and angular momentum will the orbit be a circle of radius a about the origin?

(ii) What is the period of this circular motion?

(iii) If the particle be slightly disturbed from this circular motion, what will be the period of small radial oscillations about r=a?