Modified by Ahmed

Original project Critical damping of spring

For a spring with spring constant k, attached mass m, displacement x.

The equation of motion is F=m d2x/dt2= -k*x;

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

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

The equation become m d2x/dt2+ 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

- Please feel free to post your ideas about how to use the simulation for better teaching and learning.
- Post questions to be asked to help students to think, to explore.
- Upload worksheets as attached files to share with more users.