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What is realy the idea of damped simple harmonic motion?

  1. Nov 30, 2004 #1
    i am finding damped SHM difficult to understand can anyone give sugestion as to what coul .do
     
  2. jcsd
  3. Dec 3, 2004 #2
    Damped functions

    Nearly all real world oscillating systems have some dissipatives forces. Therefore, their oscillations die out over time-unless we provide some means for replacing the dissipating mechanism. The decrease in amplitude caused by these frictional forces is called damping-and the corresponding motion is called damped oscillation.

    One can view the automobile suspension system as an oscillating system, which if not damped, would keep bobbing up and down for ever, whenever it bumped. The damped function would be an “exponential rate of decay equation x cos (w’t + phi).”

    ie Ae^(-(b/m)t) cos (w’t + phi) (1)

    Where w = sqrt (k/m – b^2/4m^2) (2)

    w’ is the angular frequency.

    The exp rate of decay is the amplitude (friction) and decreases with time because of the exponential factor e^(-(b/m)t). Note the negative sign in eq 1.

    “b” is the damping factor here. We want to make it large in this case. Look at the b^2 fraction. As b becomes large, eg the shocks pads wear out, the system: cos (sqrt (k/m – b^2/4m^2)t + phi) returns to equilibrium: cos (sqrt (k/m )).

    w becomes zero when b becomes large. (k/m – b^2/4m^2)=0
    ie b=2sqrt(km)

    When eq 2 is in 1, it is called critical damping. The system no longer oscillates when it is disturbed (eg car goes over a bump.) So we want critical damping, or underdamping for best passagenger safety.

    If b is greater than 2sqrt(km) = overdamping, no oscill. just a return to equilibrium more slowly.

    Hope this is a start.
     
    Last edited: Dec 3, 2004
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