# NTNUJAVA Virtual Physics LaboratoryEnjoy the fun of physics with simulations! Backup site http://enjoy.phy.ntnu.edu.tw/ntnujava/

## Easy Java Simulations (2001- ) => dynamics => Topic started by: ahmedelshfie on April 26, 2010, 09:09:00 pm

 Title: Critical damping of spring Post by: ahmedelshfie on April 26, 2010, 09:09:00 pm This applet about Critical damping of spring created by prof HwangModified by AhmedOriginal project Critical damping of spring (http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1085.0)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. Title: Re: Critical damping of spring Post by: ahmedelshfie on April 27, 2010, 08:25:46 pm Image from  http://en.wikipedia.org/wiki/Damping