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The motion of spring when the length of string shortened

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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.

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.

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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 ...

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