Parametric Resonance

St. Olaf College, Classical Mechanics final project

Resources:

1. "Parametric Excitation of a Nonlinear System"
W. K. Tso, Northrop Corp. and T. K. Caughey, California Institute of Technology

2. "Dynamics of Parametric Excitation"
Alan Champneys, University of Bristol

3. "On Nonlinear Dynamics of the Pendulum with Periodically Varying Length"
Anton Belikov and Alexander Seyranian, Institute of Mechanics at Moscow State Lomonosov University

4. "Parametric Excitation of Oscillations"
The Great Soviet Encyclopedia, 3rd Edition

5. "Perturbation Analysis of Parametric Response"
Ferdinand Verhulst, University of Utrecht

[chloechambers]

Hey y’all. Just popping in to say I haven’t done physics/coding in almost a decade so I unfortunately can’t help you with any current/future projects. I’m pursuing a law degree instead. All the logic of physics with none of the math.

[Dougal]

hey great video! has really helped. sorry to bother you but i am working on a very similar project and am wondering about a couple of things which could really help. firstly the damping force, most people just assume viscous damping when it is actually air resistance which is closer to velocity^2 have you have rejected bxθ' for Bx^2θ' and not b(xθ')^2 to keep it linear but closer to reality? and secondly your potential energy term p = mgx(1-cos(θ)) but would that not mean that your effective reference point would change with x as it is time dependent so it would not give a true value for the g.p.e? would mg(x0-xcos(θ)) be better, if x0 is a constant such as the maximum length of the pendulum?

i know this is probably for coursework now long forgotten and if your course is anything like mine you are very busy but it would really help me out and i would be very grateful if you could spare a moment. struggling to find decent understandable references for this stuff

[mihirparanjape]

Hi, that was a really great explanation for parametric resonance! Thanks! I had one doubt about it- In a complicated system, say a car, one component has a frequency twice that of the natural frequency of oscillation of another, would it result in an amplitude gain?

[ayanarif]

Hey it would be really helpful if i can have the code so i can run it myself too on my computer kindly help with this

[globalteamworklight]

does the amplitude rise with PHI, at n=1?

[anildubey]

Can you refer some textbooks for parametric oscillation?

[faizanhilal]

thanks..which programming language have you used?

[MarkoRimac-os]

If you decide to educate people maybe you should try speaking with a clear pronunciation of the words with commas and full stops so that a person who is trying to the learn subject can actually understand it without repating some sentences ten times.