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Author Topic: Critical damping of spring  (Read 8599 times)
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ahmedelshfie
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on: April 26, 2010, 09:09:00 pm » posted from:,,Brazil

This applet about Critical damping of spring created by prof Hwang
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.

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* Critical damping of spring.gif (18.01 KB, 869x524 - viewed 902 times.)
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ahmedelshfie
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Reply #1 on: April 27, 2010, 08:25:46 pm » posted from:,,Brazil

Image from  http://en.wikipedia.org/wiki/Damping


* Damped_spring.gif (206.61 KB, 110x359 - viewed 661 times.)
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Progress is impossible without change; and those who cannot change their minds cannot change anything. ..."George Bernard Shaw(1865-1950, Irish dramatist, essayist and critic, Nobel Prize for Literature 1925)"
 
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