The equation of motion is F=m d

^{2}x/dt

^{2}= -k*x;

The nature frequence w0=sqrt(k/m);

If damping is introduced with a form of -b*v;

The equation become m d

^{2}x/dt

^{2}+ c dx/dt + k x =0;

The behavior of the system depends on the relative values of the two fundamental parameters, the natural frequency ω0 and the damping ratio ζ=c/ (2*sqrt(m*k));

When ζ = 1, the system is said to be

**critically damped**.

When ζ > 1, the system is said to be

**over-damped**.

when 0 ≤ ζ < 1,the system is

**under-damped**.

The following simulation let you play with different parameters to view the differece between those 3 modes:

Initially, the system is set up at under-damped condition.

Drag the blue ball to the spring, you will find how under-damped look like.

Click b=b_critical to set it to critically damped condition, then click play to view the behavior.

When it is paused again, drag b to larger value to find out how over-damped look likes.

**Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop.**This work is licensed under a Creative Commons Attribution 2.5 Taiwan License

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