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Math Help - Second Order Spring Application Problem

  1. #1
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    Exclamation Second Order Spring Application Problem

    A spring is stretched 2 inches by a 3-lb weight. The weight is pushed up 3 inches above equilibrium and released. Give the equation of motion.

    I know it is an easy question, but I am not exactly sure the proper way to answer this things. Thanks guys.
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Assumptions:

    We will take the new equilibrium position as y= 0
    and points above it are -ve and below it are positive

    Steps:
    ---------
    We will use
    SHM's equation
    given by

    y= A sin(\omega t + \phi )
    -----------
    1) use equation

    kx= mg
    to get value of k, x here is 2inch

    2)
    Here since the block is initially above the new equilibrium position so we will
    have phase constant

    \phi = \frac{-\pi}{2}

    and

    3) Angular frequency is given by
    \omega = \frac{k}{m}

    4) A here stands for amplitude its = 3inch in your question


    ______________

    That's how I do it.

    Incase if you use any other position as Y = 0 than add a constant "c" in SHM's equation
    Where

    c will be given by the displacement of this new position from the equilibrium position.
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