# 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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#### Solution Preview

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.