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Linear velocity of a spring with mass

  1. Dec 20, 2011 #1
    1. The problem statement, all variables and given/known data

    why does the velocity of an small spring element will be in linear proportion to the distance from the fixed end?


    2. Relevant equations

    v(x)=[itex]\frac{x}{l}[/itex]V[itex]_{0}[/itex]


    Thank you very much,
    Tomer
     
  2. jcsd
  3. Dec 21, 2011 #2
    I would like to add my attemp (although its probably way too far from the right direction):

    the general force equation for any coordinate of a mass spring with mass M attached to it is (I think):
    L - lenght of loose spring
    z[itex]_{0}[/itex] - the lenght from the fixed wall
    Z - the coordinate of the small mass element.
    m- mass of the spring
    M - mass attached to the spring

    (M+m([itex]\frac{L-z_{0}}{L}[/itex]))[itex]\ddot{Z}[/itex]=-[itex]\frac{L}{z_{0}}[/itex]k(Z-z[itex]_{0}[/itex])

    if z[itex]_{0}[/itex] will be L then the equation will be the "normal" equation for mass M attached to a fixed spring.

    from this differential equation i've got the general velocity depends on z[itex]_{0}[/itex].
    as you can see, this is probably not the right way to approach this question - way too complicated..

    thanks, again.
     
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