Your videos are very helpful for us. Can you please solve this same broblem with matrix method with slightly change in this problem that m1 and m2 are known and m1 has less mass than m2 and also stiffness k2 is higher than k1,... Please make video on it..
Consider the undamped natural frequency of a single-degree-of-freedom linear spring-mass system. If energy dissipation is added to this system, explain whether the frequency of damped vibration will differ from the undamped one, and if so, in what manner?.......sir could you please answer this one🙏🙏🙏
Thanks for the videos, they're helping a lot! Could you explain why did you do (X2-X1) instead of (X1-X2) when calculating K2's potential energy? I'm always unsure about the order of those
One of the benefits of using the Lagrangian approach is that it doesn't matter which way round you write it because you are squaring the quantity - the signs will come out correctly regardless after plugging into Lagrange's Equations. If using the Newtonian approach, then you need to be careful to get your signs correct. Usually just a question of being consistent with your coordinates and sign conventions. My suggestion is to vary each coordinate individually and look at the effect on the spring force).
@@Freeball99 Hello loved your video i also had a question on how to incorporate damping and you cleared it up now is there a way to express the Lagrangian in terms of spring displacement? in this case it wpuld be of the second spring so xs=x2-x1
Hi. Sorry to post this message in this comment section. I am a Chinese high school student, and currently, I am working on an extended essay about tuned mass damper. I was going to do the optimization of tuned mass damper until I found it was way too complicated and beyond my ability since I have never learned this in my school. I just learn all the content on my own, but I am stuck now. Can you give me any suggestions about where to start? And how to lower the difficulty so that even high school students can finish it? Thank you very much and sorry for my poor English.
I would definitely encourage pursuing this because I think it is an interesting and relevant project. Take a look at this video I made on dynamic vibration absorbers. It should be a good starting point: ruclips.net/video/7T6pQnNBph0/видео.html The math in here requires some calculus (differential equations) for which I have some review videos: ruclips.net/video/S2-26LR8_Es/видео.html If the math in the derivations is too difficult, then simply use the final results (which are not difficult to use) and try to understand the concepts from the video. It will make a good starting point. If you have any further question regarding your project, you can drop me an email at: apf999@gmail.com ...also, take a look at "slosh tanks" for building damping.
Hi, Thanks for your Videos. @3:42 into this one I am wondering about the units... We know Energy is J which is N.m 1) gives [N/m]*[m^2] ==> [N.m] 3) gives [kg]*[m/s]^2 ==> Kg.m/s^2*m ==> [N.m] But 2) Gives [N/m/s]*[m/s]^2 ==> [N]*[m/s] ==> N.m/s Work or Energy over time is Power... Am I right?
You would just use the standard method. The only difference is that you will end up with complex eigenvalues and eigenvectors. The real part of the eigenvalue affects the damping of the system while the imaginary part of the eigenvalue affects the frequency of the system.
I assume you are talking about a geometrically nonlinear problem (as opposed to the case where say for your masses are changing). I have a few videos that start touching on the subject of nonlinear problems which include all the pendula videos and this video on the nonlinear oscillator: ruclips.net/video/l4XQtlkyC2o/видео.html
It is obvious that the resulting equations of motions are coupled because of the nondiagonal damping matrix and stiffness matrix. Solving such uncoupled system of equations is not straight forward. Can some body demonstrate how to solve such uncoupled equations?
A common way to solve coupled equations is to use the normal mode method. I need to make a video on this still, but the idea is that you can use the eigenvectors to transform the problem into its principle directions. This has the result of decoupling the equations (it diagonalizes the mass and stiffness matrices) and leaves you with n individual equations which can each be solved. Of course, you can also get solutions using the numerical methods that I have explained.
I have several videos on this. Most of the time, you will need to solve the equations of motion using numerical integration. ruclips.net/video/e1q4vD2KjpE/видео.html ruclips.net/video/r-jWnXjwQvk/видео.html
The purpose of the video was to show how to incorporate damping into the equations of motion. I have several other videos where I show how to solve equations of motion both analytically and numerically for multi degree of freedom systems..
@@Freeball99 Is it possible to get a link for the 2 degrees of freedom resolved numerically (if you made such a video) because i can only find the one degree of freedom video.
Hello! Can you please explain the eigenvalues and eigenvectors of this example!!
Thanks for this video as it explains it better than my lecturer. Are you from SA by any chance boet?
Grew up in Durban...a long time ago!
@@Freeball99 Lekker, Western Cape here!
It would be nice to have a video about natural frequencies and modes on non proportional viscous damping.
Did you find answer to your question? I had a similar issue
@@kapilpandey998 Any luck finding the answer? Can you please share if you have found it
Your videos are very helpful for us. Can you please solve this same broblem with matrix method with slightly change in this problem that m1 and m2 are known and m1 has less mass than m2 and also stiffness k2 is higher than k1,... Please make video on it..
You can simply substitute the values you have into these same equations.
Consider the undamped natural frequency of a single-degree-of-freedom linear
spring-mass system. If energy dissipation is added to this system, explain whether the frequency of damped vibration will differ from the undamped one, and if so, in what manner?.......sir could you please answer this one🙏🙏🙏
I have a video explaining this: ruclips.net/video/DErLaGaJ1d0/видео.html
Thanks for the videos, they're helping a lot! Could you explain why did you do (X2-X1) instead of (X1-X2) when calculating K2's potential energy? I'm always unsure about the order of those
One of the benefits of using the Lagrangian approach is that it doesn't matter which way round you write it because you are squaring the quantity - the signs will come out correctly regardless after plugging into Lagrange's Equations.
If using the Newtonian approach, then you need to be careful to get your signs correct. Usually just a question of being consistent with your coordinates and sign conventions. My suggestion is to vary each coordinate individually and look at the effect on the spring force).
@@Freeball99 Hello loved your video i also had a question on how to incorporate damping and you cleared it up now is there a way to express the Lagrangian in terms of spring displacement? in this case it wpuld be of the second spring so xs=x2-x1
the coordinates I mean
Hi. Sorry to post this message in this comment section. I am a Chinese high school student, and currently, I am working on an extended essay about tuned mass damper. I was going to do the optimization of tuned mass damper until I found it was way too complicated and beyond my ability since I have never learned this in my school. I just learn all the content on my own, but I am stuck now. Can you give me any suggestions about where to start? And how to lower the difficulty so that even high school students can finish it? Thank you very much and sorry for my poor English.
I would definitely encourage pursuing this because I think it is an interesting and relevant project. Take a look at this video I made on dynamic vibration absorbers. It should be a good starting point: ruclips.net/video/7T6pQnNBph0/видео.html The math in here requires some calculus (differential equations) for which I have some review videos: ruclips.net/video/S2-26LR8_Es/видео.html
If the math in the derivations is too difficult, then simply use the final results (which are not difficult to use) and try to understand the concepts from the video. It will make a good starting point. If you have any further question regarding your project, you can drop me an email at: apf999@gmail.com
...also, take a look at "slosh tanks" for building damping.
Hi, Thanks for your Videos.
@3:42 into this one I am wondering about the units...
We know Energy is J which is N.m
1) gives [N/m]*[m^2] ==> [N.m]
3) gives [kg]*[m/s]^2 ==> Kg.m/s^2*m ==> [N.m]
But
2) Gives [N/m/s]*[m/s]^2 ==> [N]*[m/s] ==> N.m/s Work or Energy over time is Power... Am I right?
Yes, you're correct. The Rayleigh's dissipation function describes the energy loss over time....so power.
@@Freeball99 "the energy loss over time" That makes sense! 🙂 Thanks mate!
How would I then find the natural frequencies and modes from this, and if I wanted to sketch the modes how would I do that.
@n Did you find the answer to this?
How would you find the eigenvalues and eigenvectors from here?
You would just use the standard method. The only difference is that you will end up with complex eigenvalues and eigenvectors. The real part of the eigenvalue affects the damping of the system while the imaginary part of the eigenvalue affects the frequency of the system.
How can use this equation to work out bush stiffness if I have the mass and frequencies but no damping coefficient???
If you have the mass and frequency, you can calculate stiffness from the frequency equation, ω = SQRT(k/m).
Hi it's a very nice video.
Do u have any video about the solution of the forced vibration of viscously damped 2DOF systems
There you go: ruclips.net/video/NV7cd-7Rz-I/видео.html
@@Freeball99 it links me to this same video is it the right link?
For the lagrange equation all the values equal = Q
After adding all the respective values it was equal to = 0
Why's that
The Qi's are the generalized forces. Since there is no force acting on m1, Q1 = 0. The applied force acting on m2 is f(t), so Q2 = f(t)
HI, thank you for the video
How can I do a non-linear analysis?
I assume you are talking about a geometrically nonlinear problem (as opposed to the case where say for your masses are changing). I have a few videos that start touching on the subject of nonlinear problems which include all the pendula videos and this video on the nonlinear oscillator: ruclips.net/video/l4XQtlkyC2o/видео.html
It is obvious that the resulting equations of motions are coupled because of the nondiagonal damping matrix and stiffness matrix. Solving such uncoupled system of equations is not straight forward. Can some body demonstrate how to solve such uncoupled equations?
sorry I meant coupled equations
A common way to solve coupled equations is to use the normal mode method. I need to make a video on this still, but the idea is that you can use the eigenvectors to transform the problem into its principle directions. This has the result of decoupling the equations (it diagonalizes the mass and stiffness matrices) and leaves you with n individual equations which can each be solved.
Of course, you can also get solutions using the numerical methods that I have explained.
@@Freeball99 What does coupled mean?
How to solve derived equation of motion ?
I have several videos on this. Most of the time, you will need to solve the equations of motion using numerical integration. ruclips.net/video/e1q4vD2KjpE/видео.html ruclips.net/video/r-jWnXjwQvk/видео.html
Thank you
why didnt you solve the last equation ???
The purpose of the video was to show how to incorporate damping into the equations of motion. I have several other videos where I show how to solve equations of motion both analytically and numerically for multi degree of freedom systems..
@@Freeball99 its nice Im gonna watch all of them..thanks for everthing...by the way I kive in the brazil and your videos are helping at the university
@@Freeball99 Is it possible to get a link for the 2 degrees of freedom resolved numerically (if you made such a video) because i can only find the one degree of freedom video.