A particle of mass m and angular momentum moves in a central spring-like force field (F=-k r).

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A particle of mass m and angular momentum moves in a central spring-like force field $F=-k r$.

(a) Sketch the effective potential energy $U_{\text {eff }}(r)$.

(b) Find the radius $r_{0}$ of circular orbits.

(c) Find the period of small oscillations about this orbit, if the particle is perturbed slightly from it.

(d) Compare with the period of rotation of the particle about the center of force. Is the orbit closed or open for such small oscillations?

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Modern Classical Mechanics

ISBN: 9781108834971

1st Edition

Authors: T. M. Helliwell, V. V. Sahakian

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Question Posted: Mar 21, 2024 12:00 AM

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A particle of mass m and angular momentum moves in a central spring-like force field (F=-k r).

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Modern Classical Mechanics

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