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Consider the mass M at the end of a massless spring whose spring constant is k and whose relaxed length is . The pendu- lum/spring is fixed at the opposite (to the mass) end, but can. freely rotate in the plane of the paper about that fixed point as shown. THERE IS NO GRAVITY FOR THIS PROB- LEM

Consider the mass M at the end of a massless spring whose spring constant is k and whose relaxed length is . The pendu- lum/spring is fixed at the opposite (to the mass) end, but can. freely rotate in the plane of the paper about that fixed point as shown. THERE IS NO GRAVITY FOR THIS PROB- LEM

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(b) •Coooooooo To 1. Consider the mass M at the end of a massless spring whose spring constant is k and whose relaxed length is l. The pendu- lum/spring is fixed at the opposite (to the mass) end, but can. freely rotate in the plane of the paper about that fixed point as shown. THERE IS NO GRAVITY FOR THIS PROB- LEM In terms of , M and the generalized coordinates r and 0, write the Lagrangian. What are the equations of motion for r and 0? List conserved quantities, expressing them in terms of r, r, 0, 0, and the pa- rameters k, l, M.
Transcribed Image Text:(b) •Coooooooo To 1. Consider the mass M at the end of a massless spring whose spring constant is k and whose relaxed length is l. The pendu- lum/spring is fixed at the opposite (to the mass) end, but can. freely rotate in the plane of the paper about that fixed point as shown. THERE IS NO GRAVITY FOR THIS PROB- LEM In terms of , M and the generalized coordinates r and 0, write the Lagrangian. What are the equations of motion for r and 0? List conserved quantities, expressing them in terms of r, r, 0, 0, and the pa- rameters k, l, M.
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