A frictionless table has a mass m on it. The table has a hole in it, where mass m is connected to a string that passes through the hole, attached to a hanging mass M. (a) What is the Lagrangian for this system? Using this Lagrangian, find the equations of motion (a = function of position) for each of the generalized coordinates used. (b) Under what conditions does m make a circular motion? (c) What is the frequency of small oscillations (in r) about this circular motion? Further, assume the oscillations are small: use a Taylor Expansion at the point we choose to use the small angle approximation.)

A frictionless table has a mass m on it. The table has a hole in it, where mass m is connected to a string that passes through the hole, attached to a hanging mass M. (a) What is the Lagrangian for this system? Using this Lagrangian, find the equations of motion (a = function of position) for each of the generalized coordinates used. (b) Under what conditions does m make a circular motion? (c) What is the frequency of small oscillations (in r) about this circular motion? Further, assume the oscillations are small: use a Taylor Expansion at the point we choose to use the small angle approximation.)

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter8: Central-force Motion

Section: Chapter Questions

Problem 8.33P

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