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Math Help - Energy in a system of springs

  1. #1
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    Energy in a system of springs

    1. Find the equation for conservation of energy in system. System consists of three springs A,B and C with stiffness k, 2k and 0.5k respectively and natural lengths l, 0.5l and 2l respectively.



    2. Relevant equations
    Equation for conservation of energy

    Datum taken at point A,

    Where is kinetic energy and is the spring stiffness and is the natural length.

    3. The attempt at a solution
    By analysing the diagam
    U_{springA}=-\frac{1}{2}k(x-l_0)^2

    U_{springB}=-\frac{1}{2}*2k(x-\frac{1}{2}l_0-\frac{1}{2}l_0)^2=k(x-l_0)^2




    My question is, is the answer and have I derived the individual energies correctly?

    Any help would be greatly appreciated, I've been banging my head against this for weeks.

    James
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by bobred View Post
    1. Find the equation for conservation of energy in system. System consists of three springs A,B and C with stiffness k, 2k and 0.5k respectively and natural lengths l, 0.5l and 2l respectively.



    2. Relevant equations
    Equation for conservation of energy

    Datum taken at point A,

    Where is kinetic energy and is the spring stiffness and is the natural length.

    3. The attempt at a solution
    By analysing the diagam
    U_{springA}=-\frac{1}{2}k(x-l_0)^2

    U_{springB}=-\frac{1}{2}*2k(x-\frac{1}{2}l_0-\frac{1}{2}l_0)^2=k(x-l_0)^2




    My question is, is the answer and have I derived the individual energies correctly?

    Any help would be greatly appreciated, I've been banging my head against this for weeks.

    James
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    CB
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