The motion of spring when the length of string shortened
Consider a simple plane pendulum consisting of a mass m connected to a string of length L.
After the pendulum is set in motion , the length of the string is shortened at a constant rate:
dL/dt = -k
The suspension point remains fixed.
Compute the following:
a) The Lagrangian and Hamiltonian functions
b) Compare the Hamiltonian and the total energy
c) Discuss the conservation of energy for the system.
Please give a through analysis
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Please see the attached file for detailed solution.
Consider a simple plane pendulum consisting of a mass m connected to a string of length L.
After the pendulum is set in motion , the length of the string is shortened at a constant rate:
dL/dt = -k
The suspension point remains fixed.
Compute the following:
a) The Lagrangian and Hamiltonian functions
b) Compare the Hamiltonian and the total ...
Solution Summary
The solution is comprised of detailed analysis of the Lagrangian/Hamiltonian of the spring when the length of the string is shortened. The total energy of the system is also discussed.