A massless spring with equilibrium length d and spring constant k connects two particles. The system is flat and horizontal, yet it may spin and vibrate (ccompress\stretch). 1- Determine the system's Lagrangian. 2- Determine the system's Hamiltonian. 3- Calculate Hamilton's equations of motion. It should be noted that the generalized momenta can be omitted. -It is worth noting that as the mass spins, it begins to expand. Hint: make your coordinate system's origin the center of the unstretched spring. also In generalized coordinates of (r_i) and (theta_i) , express your equations.
A massless spring with equilibrium length d and spring constant k connects two particles. The system is flat and horizontal, yet it may spin and vibrate (ccompress\stretch). 1- Determine the system's Lagrangian. 2- Determine the system's Hamiltonian. 3- Calculate Hamilton's equations of motion. It should be noted that the generalized momenta can be omitted. -It is worth noting that as the mass spins, it begins to expand. Hint: make your coordinate system's origin the center of the unstretched spring. also In generalized coordinates of (r_i) and (theta_i) , express your equations.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A massless spring with equilibrium length d and spring constant k connects two particles. The system is flat and horizontal, yet it may spin and vibrate (ccompress\stretch).
1- Determine the system's Lagrangian.
2- Determine the system's Hamiltonian.
3- Calculate Hamilton's equations of motion. It should be noted that the generalized momenta can be omitted.
-It is worth noting that as the mass spins, it begins to expand.
Hint: make your coordinate system's origin the center of the unstretched spring.
also In generalized coordinates of (r_i) and (theta_i) , express your equations.
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