This applet about Critical damping of spring created by prof Hwang
Modified by Ahmed
Original project [url=http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1085.0]Critical damping of spring[/url]
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 ?0 and the damping ratio ?=c/ (2*sqrt(m*k));
When ? = 1, the system is said to be [b]critically damped.[/b]
When ? > 1, the system is said to be[b] over-damped.[/b]
when 0 ? ? < 1,the system is [b]under-damped.[/b]
The following simulation let you play with different parameters to view the differece between those 3 modes:
Initially, the system is set up at [u]under-damped [/u]condition.
Drag the blue ball to the spring, you will find how under-damped look like.
Click b=b_critical to set it to [u]critically damped[/u] condition, then click play to view the behavior.
When it is paused again, drag b to larger value to find out how [u]over-damped[/u] look likes.