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 Hwang
Modified by Ahmed Original 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 overdamped. when 0 ≤ ζ < 1,the system is underdamped. The following simulation let you play with different parameters to view the differece between those 3 modes: Initially, the system is set up at underdamped condition. Drag the blue ball to the spring, you will find how underdamped 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 overdamped 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
