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Overshoot when solving damping differential equations

  1. Sep 16, 2012 #1
    I am trying to solve and plot the differential equations for springs.

    when the damping factors are under 1 (underdamping), I tried damping ratios of:
    0.01, 0.2, 0.1, 0.4, 0.8

    If I use the following equations
    (wd= damped frequency, wn= natural frequency, v0= v initial, x0= x initial, t= time)

    wd=wn*sqrt(1-z^2);
    A=sqrt(((v0+z*wn*x0)^2+(x0*wd)^2)/(wd^2));
    phi=atan((x0*wd)/(v0+z*wn*x0));
    x=A*exp(-z*wn*t)*sin(wd*t+phi);

    and when I use the initial conditions
    wn=2, x0=1, v0=1

    I get the following picture
    http://imageshack.us/photo/my-images/191/24265826.jpg/
    Why does the value of x not decrease and increase instead at the start? (Shouldn't the value of x not exceed initial value?)
    Is there something wrong with the equation I have formed above? Or is this what usually happens when solving these spring systems?
     
  2. jcsd
  3. Sep 16, 2012 #2
    You have a positive initial velocity, i.e. v0=1. If you set v0=0 what your expecting will occur.
     
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