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./htdocs/ntnujava/ejsuser/37048/users/br/ahmed/springdamping_pkg/springdamping.propertiesFull screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list

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