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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.

    Please give a through analysis

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    https://brainmass.com/physics/energy/motion-spring-length-string-shortened-99355

    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.

    $2.49

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