If you find this project interesting, there is a future for you in Engineering!
I was looking at Fbrd's 'Curve Art 3' project (an amazing project!) and I started playing around with connected dots. Then, I made them act like a series of masses connected by springs and started getting some cool vibrational behavior. So I sort of threw this project together to let people play with vibrations. It has a bunch of setups controlled by the "Change Setup button at the bottom of the screen. Here are the setups:
Jump Rope Setup: Your mouse is holding the right end of the chain, the left end is fixed. Try shaking the rope at different speeds and directions and see what shapes you can make. By shaking it slowly, you should be able to get all the dots going up and down at the same time, that is the First Vibrational Mode. Shaking at a rate about twice as fast, you should be able to get the right half dots going up while the left half is going down; that is the Second Vibrational Mode. Maybe you can find others!
Pluck Setup: The chain is fixed at both ends. Use your mouse to pluck on the dots and watch the chain respond. You could use this mode to roughly estimate the base natural frequency, if you counted vibration cycles in a given period of time.
Forced Excitation Setup: This is the most compllicated setup by FAR! Here, you control the rate at which the right end of the chain is shaken. The size of the shake is always the same but the response of the chain will vary depending on how fast it is shaken. By searching around, you should be able to find the Resonant Frequencies; these are the ones that cause the chain to vibrate the most. You can use the mouse buttons (+ and -) to move the shaker frequency or use the Left/Right arrows.
I have built in plotting capability (controlled by the Plotting On/Off button) so you can plot Peak Amplitude (how high it shakes) against shaker Excitation Frequency (how fast it is shaken). Use the Reset Peak Amp. button to reset the Peak Amplitude to zero before each reading. Then, use the Plot Point button to record a reading, when you feel the system has reached a steady state. Note that the Peak Amplitude can also be reset with the Down Arrow key and the Plot Point function can be done with the Up Arrow. Finally, the Excitation Frequency can also be set by clicking on the Graph, if you have plotting turned on.
Left/Right - Shaker Frequency
Down - Reset Peak Amplitude
Up - Plot point
Space - Next Setup