In my opinion, damping is the single best example of why complex exponents are useful. It simplifies all forms of (non-driven) damping into the single simple equation: x = Ae^(λt) (where mλ²+cλ+k = 0 for mass m, damping c, and spring constant k) It's like plucking the string of a guitar and hearing the note slowly fade, but as an equation. The mathematical elegance is literal music to my ears.
Hello Michel, I was watching your series on electrical engineering (chapter 15 - frequency response). On your amazing website it says that there should be 56 videos in the playlist but there are only 23. Have you made the other videos yet and maybe forgot to post them? You are honestly the best teacher that I know of and your videos have helped me countless times in the past! If you have already made the rest of the chapter 15 videos it would be a huge help to get to watch them. Thank you Michel once again for the effort you have put in your videos, I hope you are having an amazing day
Adam, Thank you for your nice comment. When we started making these videos (my wife and I) about 10 years ago, we didn't realize what a huge task this was going to be. We tried to cover a lot of topics, and started many playlist, and now we are going back and covering missing topics and finishing playlists we haven't completed yet. Chapter 15 is one of those playlists we still need to complete.
Acceleration is the change in velocity at that moment in time. As the object approaches the end point, the object is slowing down the most (maximum acceleration), as soon as the object reaches the end, it is being accelerated away from that point at maximum acceleration. The object spends zero time at the end point.
@@MichelvanBiezen This means 2 things: 1. Velocity shouldn't be written as (v) = zero at the ends. Instead, (a) approaches zero. 2. Acceleration has 2 directions; one with & one opposite to the velocity direction for each pathway above & below the equilibrium point. Right for both conclusions?🤔🤔
We still consider the velocity at the end points to be zero for an infinitesimal small amount of time (like we use in calculus). On "2" you are correct, but I wouldn't look at it that way. Simply look and see how the velocity is changing at the various parts of the motion.
@@MichelvanBiezen By the way, Prof. I didn't mean in (2) like you drew about the acceleration arrows in the video. I meant there should be 2 opposite arrows (2 opposite vectors) for acceleration and deceleration for the pathway above the equilibrium point and the same for the pathway below the equilibrium point. In other words, you should have drawn 4 arrows (vectors) in the video. If you don't agree, I can give you my WhatsApp number to show you my own illustration. Would you agree to presence of these 4 vectors about acceleration????🤔🤔🤔🤔
Yes it is counterintuitive. But if you hang a mass from a vertical spring and you allow the mass to be at rest at the equilibrium point there is no net force on the mass. (The force of the spring cancels out the force of gravity).
this much effort . our teacher just wrote all the formula and asked to learnt . you are amazing teacher :)
Thank you. When completed this playlist will cover all the basics about simple harmonic motion.
This channel is gold mine 😁...
I have great respect for you that you have uploaded so much quality content for free.
Glad you are enjoying the videos. We appreciate the comment. 🙂
In my opinion, damping is the single best example of why complex exponents are useful. It simplifies all forms of (non-driven) damping into the single simple equation:
x = Ae^(λt)
(where mλ²+cλ+k = 0 for mass m, damping c, and spring constant k)
It's like plucking the string of a guitar and hearing the note slowly fade, but as an equation. The mathematical elegance is literal music to my ears.
Stay tuned. We'll get to the damping equations soon.
I am from Egypt and I would like to tell you that your explanation is beautiful and good luck
Thank you! 😃 And welcome to the channel!
That was a great explanation of the equivalence of the oscillatory motion!
Thank you. We plan on a playlist describing the fundamentals of simple harmonic motions including damping.
Hello Michel, I was watching your series on electrical engineering (chapter 15 - frequency response). On your amazing website it says that there should be 56 videos in the playlist but there are only 23. Have you made the other videos yet and maybe forgot to post them? You are honestly the best teacher that I know of and your videos have helped me countless times in the past! If you have already made the rest of the chapter 15 videos it would be a huge help to get to watch them.
Thank you Michel once again for the effort you have put in your videos, I hope you are having an amazing day
Adam, Thank you for your nice comment. When we started making these videos (my wife and I) about 10 years ago, we didn't realize what a huge task this was going to be. We tried to cover a lot of topics, and started many playlist, and now we are going back and covering missing topics and finishing playlists we haven't completed yet. Chapter 15 is one of those playlists we still need to complete.
Nagyon érthetően és tömören levezetett differenciális egyenletek a harmonikus rezgéshez. Köszönöm.
Glad you liked it.
Cool stuff! Fits right in to my study of mathematics in music! Thanx! ❤ 😊
Glad you like it!
Thank you, the explanation is very good, lots of words, but well done. I like this better than mutual inductance🙂
You are welcome!
lol i was studying SHM and this vid popped up. Man youtube be listening its users . Thanks for the explanation sir
You are welcome. There is more to come. Also, we already have several complete playlists with examples on this channel.
@@MichelvanBiezen ooh thanks will check that out too :).
This is the basic for earthquake engineering.
Thank you.
Yes indeed.
Thanks for the help and wholehearted efforts that you give us .
Thanks forever my beloved sir ❤️
It is our pleasure. We are glad that our work is appreciated.
Good to see damping used properly. Even those who should know better say dampening.
Thanks for the insight
I love his bow-tie 😄 Super oulik
Thank you. 🙂
Very well professor . Keep uploading videos on youtube
We plan on completing this playlist.
thank professor it is great work
You are welcome. Glad you find it helpful. 🙂
I have a question in which cases cosine or sine becomes
In the United States trigonometry (sine and cosine) are introduced in high school.
Nice I have a question how I can send you the picture
We have had viewers that were able to send pictures in a link on the comments.
@@MichelvanBiezen I post 2 links with google drive link but it is not working it keep deleting my comment
Yes, youtube has a filter where they will delete "suspect" attachments. I do have receive such attachments in the past from viewers with questions.
What is the unit of the big A?
A is the amplitude of the motion. In MKS units it would be meters. But you can use any other unit if appropriate.
@@MichelvanBiezen thank you
Hello, dear Professor
How mathematically can be the acceleration (a) present while the velocity (v) = 0 at maximum amplitudes?🤔🤔🤔
Acceleration is the change in velocity at that moment in time. As the object approaches the end point, the object is slowing down the most (maximum acceleration), as soon as the object reaches the end, it is being accelerated away from that point at maximum acceleration. The object spends zero time at the end point.
@@MichelvanBiezen This means 2 things:
1.
Velocity shouldn't be written as (v) = zero at the ends. Instead, (a) approaches zero.
2.
Acceleration has 2 directions; one with & one opposite to the velocity direction for each pathway above & below the equilibrium point.
Right for both conclusions?🤔🤔
We still consider the velocity at the end points to be zero for an infinitesimal small amount of time (like we use in calculus). On "2" you are correct, but I wouldn't look at it that way. Simply look and see how the velocity is changing at the various parts of the motion.
@@MichelvanBiezen By the way, Prof. I didn't mean in (2) like you drew about the acceleration arrows in the video. I meant there should be 2 opposite arrows (2 opposite vectors) for acceleration and deceleration for the pathway above the equilibrium point and the same for the pathway below the equilibrium point.
In other words, you should have drawn 4 arrows (vectors) in the video.
If you don't agree, I can give you my WhatsApp number to show you my own illustration.
Would you agree to presence of these 4 vectors about acceleration????🤔🤔🤔🤔
Thnku
You are welcome.
It is curious that gravity does not play a role in the equations,not too intuitive 😅
Yes it is counterintuitive. But if you hang a mass from a vertical spring and you allow the mass to be at rest at the equilibrium point there is no net force on the mass. (The force of the spring cancels out the force of gravity).