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Damped Oscillation problem.

  1. Sep 1, 2010 #1
    1. The problem statement, all variables and given/known data
    Help need with this problem.

    A light spring AB of natural length 2a and of modulus of elasticity 2amn2 lies straight at its length and at rest on a smooth horizontal table. The end A is fixed to the table and a particle P of mass m is attached to the midpoint of the spring. The end B is then caused to move along the line AB so that after a time t the distance between A and B is a(2+sinnt). Denoting the distance of P from A by a+x, show that
    d2x/dt2 + 4n2x = 2an2sinnt.
    Find the value of t for which P first comes to rest.


    3. The attempt at a solution
    Here's my attempt so far, can't find the value of t for which P first comes to rest.
    Am I right or wrong. Anyone has a better solution and a solution to the second part.

    AB = 2(a+x) since AB at rest is twice a+x

    At t, AB = 2a + asinnt

    F = -k(x-e) where e is the extension and x the natural length

    = k(e-x)
    ma = 2amn2/a (2a + asinnt -2a - 2x)

    a = 2n2 (asinnt - 2a)

    = 2n2sinnt - 4n2x

    a + 4n2x = 2n2asinnt

    => d2x/dt2 + 4n2x = 2n2asinnt
     
  2. jcsd
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