I am a practicing aerospace engineer. I specialize in structural analysis but recently I have been given some vibration analysis, specifically harmonic analysis to perform per DO-160G. Typically, as the process goes, you would begin with a modal analysis which I did. And then you would perform the Harmonic using the modal results as a reference. While I see the process I am meant to follow, I saw the equation I need to use in the form of equation 2 (in your lecture) But I have been wondering what the genesis of that equation is. Although I realize it was from solving the differential equation arising from the problem, I did not realize that it was from a combination of the cosine and sine curves. This was a revelation. I am so glad I “stopped working” for a few minutes to dig into the details of the equation I was working with. We live and we learn everyday and today I learned something very valuable from you. Thanks so much and keep up the good work.
This is a phenomenal, mind-blowing explanation! This beautifully explained visually what I was learning in the past weeks particularly at 15:54 when you smoothly transitioned to x(t) = X•cos(wt - phi) after substituting C1 and C2 in terms of phi.
Just a question for me. I understood everything and it is clear, thanks for this but with the trigonometric circle, I don't really understand why the part with cosine is on the "y axis" and the part with the sine on the "x axis" ? 5:43
This is because I am projecting the length of the vector horizontally (onto the y-axis). Thus, initially cos 0 = 1 and sin 0 = 0. So initially, the cosine vector points along the y-axis so that it projects it's full height (imagine I have a light source on the left which is casting a shadow of the vectors onto the y-axis on the right). Alternatively, if I chose instead to project this downward onto the x-axis (imagine now the light source is above) then in this case, initially the cosine vector would point in the direction of the x-axis instead and the sin vector would point in the NEGATIVE y-direction. Note that in this case, the cos vector still leads the sin vector by 90 degrees. Hope this helps and that I haven't confused you.
@@Freeball99 Yes I see better now I think. I was troubling because it was not really like the mathematical trigonometric circle but no matter, we have to look this circle with the graph on the right and the physical meaning of oscillations/vibrations. Thanks for your good answer :)
I have a quick question: Are there sorts of problems where using newton's method is preferable to the Lagrangian for deriving EOM's? Like, are there special cases in vibrations where F=ma is better? I would assume Newton's becomes easier inversely proportional to the complexity of the system? Like, using the Lagrangian on a projectile physics problem would be overkill.
I've read it in a couple of books - one of which is old and now out of print. I've never seen anyone else teach it this way in person or video and, frankly, have never understood why not!
In general, no they are not equal. W is the frequency of the forcing function (ie the frequency that we are try to force the system to vibrate at) where Wn is the natural frequency of the system (ie the frequency that the system wants to vibrate at). Wn is totally independent of the force being applied - it is a property of the system. When W = Wn then resonance occurs (generally an undesirable effect).
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I've taken difEQ, analytics for ECE and am now struggling through Vibrations. I didn't understand this until this single 20min vid. you have a gift.
Glad it was helpful!
I am a practicing aerospace engineer. I specialize in structural analysis but recently I have been given some vibration analysis, specifically harmonic analysis to perform per DO-160G.
Typically, as the process goes, you would begin with a modal analysis which I did. And then you would perform the Harmonic using the modal results as a reference.
While I see the process I am meant to follow, I saw the equation I need to use in the form of equation 2 (in your lecture)
But I have been wondering what the genesis of that equation is.
Although I realize it was from solving the differential equation arising from the problem, I did not realize that it was from a combination of the cosine and sine curves. This was a revelation.
I am so glad I “stopped working” for a few minutes to dig into the details of the equation I was working with.
We live and we learn everyday and today I learned something very valuable from you.
Thanks so much and keep up the good work.
What a video.
I appreciate you trying to make a nice freehand cosine curve.
This is a phenomenal, mind-blowing explanation! This beautifully explained visually what I was learning in the past weeks particularly at 15:54 when you smoothly transitioned to x(t) = X•cos(wt - phi) after substituting C1 and C2 in terms of phi.
Best explanation for this subject. You can't find It só simple as exposed in textbooks. Great job. Greetings from Brazil.
the world need more men like you sir thank you
So nice of you.
Just a question for me. I understood everything and it is clear, thanks for this but with the trigonometric circle, I don't really understand why the part with cosine is on the "y axis" and the part with the sine on the "x axis" ?
5:43
This is because I am projecting the length of the vector horizontally (onto the y-axis). Thus, initially cos 0 = 1 and sin 0 = 0. So initially, the cosine vector points along the y-axis so that it projects it's full height (imagine I have a light source on the left which is casting a shadow of the vectors onto the y-axis on the right).
Alternatively, if I chose instead to project this downward onto the x-axis (imagine now the light source is above) then in this case, initially the cosine vector would point in the direction of the x-axis instead and the sin vector would point in the NEGATIVE y-direction. Note that in this case, the cos vector still leads the sin vector by 90 degrees.
Hope this helps and that I haven't confused you.
@@Freeball99 Yes I see better now I think. I was troubling because it was not really like the mathematical trigonometric circle but no matter, we have to look this circle with the graph on the right and the physical meaning of oscillations/vibrations.
Thanks for your good answer :)
What software and device is that sir, it looks great. Just like your explanation
App is called "Paper" by WeTransfer. It is running on an iPad Pro 13 inch and I am using an Apple Pencil. Screen is recorded using Quicktime.
I have a quick question: Are there sorts of problems where using newton's method is preferable to the Lagrangian for deriving EOM's? Like, are there special cases in vibrations where F=ma is better? I would assume Newton's becomes easier inversely proportional to the complexity of the system? Like, using the Lagrangian on a projectile physics problem would be overkill.
how did you come up with this kind of explanation? Was it teach by your teacher? Amazing explanation
I've read it in a couple of books - one of which is old and now out of print. I've never seen anyone else teach it this way in person or video and, frankly, have never understood why not!
@@Freeball99 Name of the book please?
@@adheensheikh6896 Mechanical Vibrations by S.S. Rao
@@Freeball99 can I get it in pdf format online
@@adheensheikh6896 A Google search for "mechanical vibrations ss rao pdf" returns several results.
is W =Wn ????
In general, no they are not equal.
W is the frequency of the forcing function (ie the frequency that we are try to force the system to vibrate at) where Wn is the natural frequency of the system (ie the frequency that the system wants to vibrate at). Wn is totally independent of the force being applied - it is a property of the system. When W = Wn then resonance occurs (generally an undesirable effect).