Critical damping of spring

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.

Embed a running copy of this simulation

Embed a running copy link(show simulation in a popuped window)

Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop. This work is licensed under a Creative Commons Attribution 2.5 Taiwan License

Please feel free to post your ideas about how to use the simulation for better teaching and learning.
Post questions to be asked to help students to think, to explore.
Upload worksheets as attached files to share with more users.

Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics!

Related Topics
	Subject	Started by	Replies	Views	Last post
	Pendulum with damping Dynamics	Fu-Kwun Hwang	0	15614	June 25, 2008, 01:10:08 pm by Fu-Kwun Hwang
	Critical damping of spring Dynamics	Fu-Kwun Hwang	0	18572	April 12, 2009, 04:41:25 pm by Fu-Kwun Hwang
	vertical spring in equilibrium (adjustable gravity,spring constant and mass) Dynamics	Fu-Kwun Hwang	3	12061	May 17, 2019, 03:05:19 pm by angelinajolie
	Similarity between RLC circuit and spring with damping Electromagnetism	Fu-Kwun Hwang	2	23344	July 30, 2020, 10:06:51 pm by mahi01
	Similarity between RLC circuit and spring with damping electromagnetism	ahmedelshfie	7	8184	April 19, 2010, 12:00:27 am by Fu-Kwun Hwang

	Author	Topic: Critical damping of spring (Read 9126 times)
0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).