Overshoot when solving damping differential equations

  • Thread starter max1546
  • Start date
  • #1
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Main Question or Discussion Point

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?
 

Answers and Replies

  • #2
117
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You have a positive initial velocity, i.e. v0=1. If you set v0=0 what your expecting will occur.
 

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