Exponential Response - Possible Resonance

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MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
View the complete course: ocw.mit.edu/RES...
Instructor: Gilbert Strang
Resonance occurs when the natural frequency matches the forcing frequency - equal exponents from inside and outside.
License: Creative Commons BY-NC-SA
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Опубликовано:

21 окт 2024

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Комментарии : 9

@chnegsi 7 лет назад

'we have to drag L'Hopital from hospital and do it again...' LOL

@francine8563 3 года назад

thank you so much sir! Heroes truly don't wear capes, heroes are the educators!

@atomskyjahid1533 8 лет назад

Throughout these lectures, I felt like I'm relearning physics. :)

@hathuytu 3 года назад

this way of solving the ode could lead to the case that y= -t*exp(s1*t)/(2A*s1+B) is also a perticular solution. It looks like this is a trick, not a method to solve this ode. There are two other perticular solutions as well.

@zizo-ve8ib 3 года назад

But where did the 2nd e^s1t go ? And does the 1/(2As1 + B) give us a 1 ?

@Labroidas 3 года назад

I really didn't get that last part at all. I feel like there is a hole in the explanation, the video is over a little too quick. I tried solving my homework with this method and it didn't work at all for me.

@gabrielbrunoparreira5670 3 года назад

kind of late response so you probably already figured it out by now haha. But anyways this is how I understand it: It seemed like they were more like partial derivatives. He derived the functions with respect to s and treated t as a constant. That is why on the first one you have the exponential multiplied by t. The second equation would be just a constant because s1 is a constant and t is also a constant, so the derivative is 0.

@rakhimovv Год назад

In case of resonance: y(t) = y_null + y_particular = c_1 * e^{s_1*t} + c_2 * e^{s_2*t} + c_3 * t * e^{s_1*t}. Further if also s2=s1 then: y(t) = y_null + y_particular = c_1 * e^{s_1*t} + c_2 * t* e^{s_1*t} + c_3 * t^2 * e^{s_1*t}.