Resounding Success

Earlier this week, I was getting ready to do some baking, but noticed something strange when I set out my mixing bowl:

 

There appears to be some vibration in my apartment that the fork/bowl were picking up.  I shared the video on Facebook, and joked that perhaps a passing gravitational wave was responsible, but when I heard my nephew was interested, I decided to go a little more in-depth.

The reason the fork begins to rattle is that the vibration is near the fork's resonant frequency.  This is the frequency at which a system is best able to absorb energy.  This may sound complicated, but you already have experience with finding a resonant frequency if you've ever played on a swing-set.  The way you pump your legs, pushing forward and pulling pack, is exactly the type of motion I'm talking about.

As a physics student, I've had many opportunities to experiment with resonant frequencies in labs, and get a feel for how the different parameters interact.  I wasn't sure how helpful it would be to show you a few isolated examples, and I wondered how difficult it would be to design an interactive experiment in HTML5.  Thanks to the examples by Daniel Schroeder (who coincidentally wrote the thermal physics textbook I used a few years ago), I was able to put together a simple demo in a matter of hours!

Below, you'll find an animated pendulum with some sliders.  The pendulum has 3 forces acting on it: gravity, which is always pulling it toward its lowest point; a damping force, which slows the pendulum according to its current speed; and a sinusoidal driving force, which pushes and pulls the pendulum with a specific amplitude and frequency (think of the leg-pumping on the swing).

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Damping

Driving Amp

Driving Freq

The units are set up such that the pendulum's natural frequency is 1.  With no damping, this is the same as the resonant frequency, but adding damping brings the resonant frequency down.  I found (0.2, 0.3, 0.9) to be a good set, but the whole point is to play around a bit.  Be sure to leave a comment if you find a particularly interesting setting!

I was amazed how simple it was to make this in HTML5, so I may do more of these in the future.  If you'd like to take a look, I've put a stand-alone version here, so you don't need to go digging through the page source.