- #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?

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?