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Spring with Mass

  1. Aug 3, 2006 #1
    Suppose a spring with mass m and length L is connected to a rigid wall and a mass of M. Assuming no damping how do we find the frequency?

    for the spring Density = m/L = D; dm = D dx
    I don't know where to go from there.
  2. jcsd
  3. Aug 3, 2006 #2
    The effective mass of a spring undergoing oscillatory motion is considered
    to be 1/3 the mass of the spring. For any portion of the spring the
    KE of dm is 1/2 dm * v^2. For a spring fixed at one end the velocity of an
    element dm will be proportional to the distance from the fixed end - so
    v = V*(y/Y) where Y is the length of the spring and V is the velocity of the moving end. Also, you can write dm = M * (dy/Y). Using these values
    integrate 1/2 v^2 dm over the length of the spring to get the KE of the
    oscillating spring and determine the effective mass of the spring.
  4. Aug 5, 2006 #3
    Thanks, I understand now.
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