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Damped Harmonic Oscillation

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If you look to the right side of this website, you may notice something unusual. As you scroll down the page, the pesky ad-bar on the side of the screen just wont go away! Ignoring it won’t help, that thing is persistent!

After your initial annoyance wears off, you may also notice something very cool. The ad is bouncy! Instead of just moving to the new position, it acts like its on a spring.

Of course, maybe this is the first time you’ve noticed any of this. Nevertheless, you are aware of it now and you will be told how it does it’s bouncy thing.

Damped Harmonic Oscillation: This is how its done. This is basically a big term for a simple concept. If you compress a spring and let it go, it will bounce back to past its original size, then compress part of the way again, and repeat this a couple of times.
With each pass though, these bounces (or oscillations) get smaller and smaller until the spring stays still, at its uncompressed size.

With out the “Damped” part, this spring would continue to bounce (or oscillate) the same height each time with no reduction in bounce height. Damping reduces the distance traveled with each rebound.

So now, before we dive into any more math and science, heres a little something to wet the beak.

There are three variables in this little program, and here is what they do.

• Mass: The mass here is the wheely thing. As you increase the mass, momentum increases linearly. The final result is more bounces, this is because more momentum means more energy to overcome the energy in the spring. Try increasing it to get maximum bouncing but slower acceleration.
• Spring Constant (K): Some springs are stiffer than others. This is the chief reason for insecure limp springs. Adjust the strength of your spring with this variable.
• Damping Constant: Think of this variable as brakes on the wheel. As this increases, each bounce decreases just like you’ve increased the brakes.

How does all this translate to oscillating linear translation? If you really want technical details, I would suggest wikipedia or Hyper Physics

In class, I always sleep through the derivation and write down the final equation… I feel like it would be the same here. So without further ado, here is the driving equation.

Calculate (1) and (2), use these in Equation (3) to get the position at a given time t.

2 Responses to “Damped Harmonic Oscillation”

1. dawn says:

   April 5, 2009 at 10:21 am

   wow!
2. Joshua says:

   November 19, 2009 at 10:01 am

   Cool, man! I understand how it works (to a layman’s level) but not how you would use this in a technical situation? I mean, there would be friction and gravity to work with too, if ever put to actual tests. Perhaps that’s why you have it horizontal.