Overshoot when solving damping differential equations

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The discussion focuses on solving and plotting differential equations for spring systems underdamped with various damping ratios. The user is puzzled by the behavior of the displacement, x, which initially increases instead of decreasing, despite expectations based on initial conditions. The equations used include the damped frequency and amplitude calculations, with specific initial values for natural frequency, displacement, and velocity. The observed behavior is attributed to the positive initial velocity, indicating that the system's response can exceed the initial displacement. This outcome is typical in underdamped systems when initial velocity is not zero.
max1546
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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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