Chapter 04.10: Lesson: A Physical Example of Application of Eigenvalues and Eigenvectors

[carmelpule]

First of all, I wish to congratulate this gentleman for his clarity in explanation and also his absolute control on his handwriting which indicates so clearly that his mind is perfectly stable and that he took care of himself in not thinking that an academic qualification is enough. His voice control and his manipulations and the levelling of his handwriting is excellent in every manner.

About the demonstration of this solution, while this is good manner in which to teach the dynamic problem shown on the board, I am a little hesitant to show it in this manner as one misses the transient part and also the different modes of oscillations that such a system can enter. Also I am not sure that the phase shift of the system can be said to be the same for both masses as during the transient period before it all settles down to steady state, which is the solution the lecturer suggests, well I feel that there is a lot of missed " engineering " in such a solution.

From the point of view of teaching eigenvalues and eigenvectors well this is the method to use, but from a student's point of view I found that it would be more informative to program the two equations on a computer with the associated two integrals for each equation and through an iterative programme one can see the build up of the transient and the steady state condition in addition to seeing the different modes of oscillations if the masses are started in different directions.

To make early assumptions of the solutions I find that it could be rather weak in illustrating the richness of such a system starting from scratch for different starting conditions. I suppose the method used depends whether one is trying to illustrate the mathematics of the system or the engineering or physics of the system. Both are useful, and both contain information that are otherwise hidden if one does not use mathematics or more detailed physical solutions due to caring about the starting transients, the possible modes of oscillations and of course the resulting steady state with all the phase shifting and lagging and leading of phase shifts of one mass with respect to the other. Also if this was a real practical problem, the distances with which the springs would settle down are not contained in the above solution. Perhaps a little inclination of the floor would add more knowledge to the student as to the final settling of the system.

[linokl]

The best explanation of the physical meaning in the world...no one explains it better

[earfunk]

Great explanation ... have calculated eigenvalues in undergrad and never really visualized their practical use. This was very enlightening as to their value in real applications. Thanks.

[ammadurrahman]

I am student of econometric, and was searching for use of eigen values. This physical example help me to understand it conceptually.

[leebraiden]

Point 12:55 on the video states that you have divided both equations by 15. Yet if you divide both equations by 15, you do not get the numbers you have stated. it appears that you have divide equation 1 by 10 and equation 2 by 20 in order to get the numbers you state. Can someone explain this to me please. Is it a mistake in order to force the Omega's into having no coefficients infront of them, thus making the matrix work, or am i missing something here??, i.e. 30 / 15 does not equal 3. I am confused ????

[sinandemir]

This is a very solid and well defined example of Eigenvalue problem. Thank you! 

[getahunhaile]

Excellent lecture thanks, but you did not explain why you say are eigenvalue and eigenvector. Maybe a plot of the data will help.

[alexramirez]

That's awesome...new connections in my mind made were made ...thanks!

[nidhirrr]

Great explanation. But what is the system has one damper in it.? What will be the assumed solution equation. ? Can i follow same method ?

[adochshanov]

Tremendously clear object-lesson! Thank you!

[bartonpaullevenson]

There seem to be a lot of steps in this presentation that are not clearly justified. For example, how did he take omega-squared out of the a and d terms in the A matrix when they were part of a sum? This comes off as rushed and, as a result, unclear.

[agnesasopaj]

Hello! Could you please also explain the Eigenvalues and Eigenvectors if the system also has 2 dampers.

[miamisasquatch]

Does this imply that the eigen value(s) is the speed/frequency a system rotates/oscillates about the eigen vector(s)?

[avinashbaliyan]

Thank you for the mathematics part, but what we deduced from this, i mean why we calculated eigen vector, eigen value ? i am wandering since 4 hrs now on net to understand it, no one is able to explain it properly, alas ...!

[thomasolson]

I'm interested in mixed unit geometry. I think for it to exist, there has to be some kind of underlying equivalence that must be set.

[minhthien]

i appriciate your lecture. i have a question that are there any conditions of A1 or A2? And if you can, pls give an example with real number. Thanks

[brideysimon]

I’m waiting for that fire alarm to go off...

[jmelojr]

Not good.. algebra mistakes, noticeably in the end w2 was factored out of matrix A

[rishabhshar]

i literally find it out, the lambda value is -0.308

[rohit]

You wasted my 15 min. Where was the physical significance with real world question ?