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Math Help - Spring in water problem

  1. #1
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    Spring in water problem

    Hi,

    Can anybody help with solving this problem? Thanks.

    A point particle of mass m is attached to a spring of spring constant k which is pulled with constant acceleration A. The spring lies along the direction of the acceleration A and the system is immersed in a fluid, so that when the mass moves with velocity v, it is subject to a viscosity force fv = βv, which opposes its motion.
    a. Write down, without solving it, the equation of motion for the mass in a reference frame moving with the system.
    b. Neglecting the viscosity, compute the elongation of the spring at equilibrium and the period of the oscillations of the mass.
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  2. #2
    Super Member fardeen_gen's Avatar
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    A point particle of mass m is attached to a spring of spring constant k which is pulled with constant acceleration A. The spring lies along the direction of the acceleration A and the system is immersed in a fluid, so that when the mass moves with velocity v, it is subject to a viscosity force fv = βv, which opposes its motion.
    a. Write down, without solving it, the equation of motion for the mass in a reference frame moving with the system.
    a. Assuming the motion is such that gravity is not involved (horizontal motion) the basic equation is

    ∑F = m*dx/dt

    The forces are the spring force in the positive direction = k*x and the viscosity force in the negative direction = -β*v.

    k*x - β*v = m*dx/dt


    Since v = dx/dt the equation becomes

    m*dx/dt + β*dx/dt - k*x = 0

    or

    dx/dt + β/m*dx/dt - k/m*x = 0

    EDIT: The reference is the anchor point of the spring. The mass is not stationary with respect to that.
    Last edited by fardeen_gen; April 25th 2009 at 11:06 PM. Reason: Clarification
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