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Harmonic motion, 2 masses

  1. Apr 1, 2005 #1
    Urgent! Damped Simple Harmonic Oscillation

    The thread topic says 2 masses, but there is actually only one!
    I'm not asking for the complete solution for this problem; I simply just don't know WHERE to start.... The question is as follows:

    In Figure 15-15, a damped simple harmonic oscillator has mass m = 290 g, k = 70 N/m, and b = 75 g/s. Assume all other components have negligible mass. What is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 20 cycles (Adamped / Ainitial)?

    The figure shows a "Rigid support" at the top, to which a spring is hooked. At the bottom of this spring is a rectangular mass. At the bottom of this mass extends a vane which falls into water as the spring elongates.

    variables listed: k, m, b (damping constant)
    Please help if at all possible!
     
    Last edited: Apr 1, 2005
  2. jcsd
  3. Apr 2, 2005 #2

    Andrew Mason

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    Homework Helper

    The solution to the differential equation of motion:

    [tex]m\ddot x + b\dot x + kx = 0[/tex] is

    [tex]x = A_0e^{-\gamma t}sin(\omega t + \phi)[/tex]

    where [itex]\omega^2 = \omega_0^2 - \gamma^2 = k/m - b^2/4m^2[/itex]

    What is the time, t, after 20 cycles? (ie. [itex]\omega t = 40\pi[/tex]?)

    What is [itex]\gamma t = bt/2m[/itex]?

    What is the amplitude (maximum x) at this time?

    AM
     
    Last edited: Apr 2, 2005
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