Second order differential equations and analog computers

[bitrex]

Hey everyone, I've been doing some experiments with analog computers to further my knowledge of op-amps (and second order differential equations!) This is more of a mathematical question than an electrical engineering question, so I thought I'd ask it in this section. I'm looking for some suggestions for differential equations that describe physical systems that would be fairly easy to implement as analog circuits - I've done the spring-mass-damper system and it's nice to see the output on the scope oscillate around in response to a step input in a very underdamped system. Any suggestions for other differential equations (of second-order or other) that might be interesting to implement? Ideally they would not involve nonlinear terms and there wouldn't be too many total terms as it's difficult to wire up too many op-amps!

 

[berkeman]

Fun project. I googled second order differential equations, and got some good hits. Here's an interesting one discussing applications (like the damped spring you've done already:

http://www.stewartcalculus.com/data... Contexts/upfiles/3c3-AppsOf2ndOrders_Stu.pdf

You might re-do that google search to look for more applications.

 

[bitrex]

One of the interesting results I figured out from playing with these circuits is that "Hey, this analog computer circuit looks a lot like a state-variable filter. Wait, it IS a state variable filter!" Each of the outputs that correspond to the acceleration, velocity, and position correspond to high pass, band pass, and low pass respectively. I could also use this circuit as a crude analog percussion synthesizer - instead of a resistor in the feedback loop that corresponds to the 1/m term I could use something like the LM13700 operational transconductance amp as a variable resistor. By changing the 1/m term I would change the frequency of the undamped oscillation. Thanks for the PDF file link, I'm going to hang on to that one for reference.