Overshoot when solving damping differential equations

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SUMMARY

The discussion focuses on solving and plotting damping differential equations for spring systems, specifically underdamped scenarios with damping ratios of 0.01, 0.2, 0.1, 0.4, and 0.8. The equations used include the damped frequency (wd), natural frequency (wn), and initial conditions (v0=1, x0=1). The user observes that the value of x initially increases instead of decreasing, which is explained by the positive initial velocity (v0=1) affecting the system's behavior. Setting v0 to 0 results in expected behavior where x does not exceed the initial value.

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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?
 
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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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