The equation of motion is F=m d[sup]2[/sup]x/dt[sup]2[/sup]= -k*x;

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

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

The equation become m d[sup]2[/sup]x/dt[sup]2[/sup]+ 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/2/users/ntnu/fkh/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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