Coupled oscillators | Lecture 46 | Differential Equations for Engineers

Differential equations for two masses connected by three springs to walls.
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[@ProfJeffreyChasnov]

Find other Differential Equations videos in my playlist kzbin.info/aero/PLkZjai-2JcxlvaV9EUgtHj1KV7THMPw1w

[@freemanfreed1581]

i do not understand x2-x1 or x1-x2 !!! why we are not allowed to write as k(x2-x1) for the first mass)

[@radiatedracer3830]

FBD should be first.

[@Saint_Studios]

Thank you for this great explanation. Helping me get through my homework at 3 am

[@rayquoiz5822]

same

[@janeknox3036]

If anyone is interested in knowing how he writes backward - its because its a mirror image. I have seen many people do this and I find it improbable that they are all left handed. Hes actually right handed.

[@ProfJeffreyChasnov]

Haha! There must be some left-handed mathematicians!

[@janeknox3036]

Jeffrey Chasnov This question pops up in comments in every video where someone writes like this. They almost all appear to be left handed, which seems statistically unlikely. Therefore they are most likely right handed just reflected.

[@mathematicianjeff8358]

I am going for my masters in applied mathematics, and I never really used used Hooke's law before. I took Physics in undergrad, but excellent explanation on how to create the ODE. After that, I know how to solve, but needed the setup. Thanks!

[@Inferior_Machines]

kzbin.info/www/bejne/lXnXe4Wdnr2pgJY check out: (vertical Newton’s cradle with Hooke’s spring mass system) Compare Newton’s law of acceleration vs Hooke’s law of acceleration on the y-axis. Hooke won.

[@maxrybold1531]

I am watching this as a review for such a system, and it is very well done, so thank you! I would preferably write out the summation of force acting on m, yet you defined each force so it is adequate to skip that step I guess.

[@henrytu3720]

am I the first one asking how you could write on the mirror side?

[@swapnilholkar8251]

I am from India 🇮🇳🇮🇳🇮🇳

[@cobblebrick]

No one cares

[@HIMANSHUHARSHIT]

padhhle bsdkkkkkkkkkk

[@dionysisevripidou2256]

Best explanation i have seen. Thank you!

[@TheTurkey72]

If there was a third mass there, would you have to take that in account for each equation of motion? Like would it be (x1-x2) still or would it have to be something like (x1-x2-x3)?

[@ProfJeffreyChasnov]

There would be three equations instead of two. Only the springs attached to masses need to be taken into account for the forces.

[@TheBigFatVladimir]

The force on mass 2 should be -kx2+K(x2-x1) right?

[@rabbisadick6292]

THE EXPLANATION IS VERY GOOG

[@한두혁]

Hello. I have a question. How do you know whether its x2-x1 or x1-x2? (in the first eq of motion) This confuses me

[@ProfJeffreyChasnov]

Think about the direction of the force when x2 is larger than x1

[@한두혁]

I got it thank you!

[@karanpai9]

Thank you for the great explanation!

[@iamsosweetgahayah2977]

Sir thank you

[@gurbanliye]

He writes backwards, I wish I could do it one day

[@nootums]

He writes normally. he mirror flips the image after recording

[@ancientgear7192]

It's a special software.

[@yashagnihotri6901]

2 min. silence for such people !

[@physicswalebaba1942]

Sir love from india.😊

[@hasnnajm8345]

*FOR THOSE WHO DOESN'T KNOW MATRIX* u can solve it by taking z1=X1"-X2" , and Z2=X1"+X2" and then deducing the Z1(t) which respond for {X1+X2}(t) and Z2 which respond for {X1-X2}(t) by adding Z1(T)+Z2(t)=Z1+Z2 we can determine the equation of X1 then w1, by taking Z1(t)-Z2(t)=Z1-Z2 WE CAN DETERMINE the general equation of X2 and then w2 ..

[@eliteteamkiller319]

Wait... do you mean to tell me this guy is writing backwards? .... Inb4 it the video is flipped.

[@andersolofsson2841]

4:03 I don't understand this part. Wouldn't the force of the second spring be directed in the opposite direction? I feel like the two springs would be pulling in the same direction if both terms in the equation are negative.

[@goofi953]

How did you create the Matlab simulation?

[@ProfJeffreyChasnov]

GUI in MATLAB. You can download it from their file exchange.

[@secularbanda1808]

Thanks for this beautiful lecture...Alien❤😅👍

[@datchentai3047]

Excellent presentation and explanation Thank you!

[@sashaguzman7792]

YOu're amazing, Thank you so much

[@benvanhuyssteen4758]

Thank you!! Brilliant simple explanation

[@salvatoremanfredid115]

Amazing! Thanks

[@tianlouw8505]

What if it wasn't a spring force between the masses, but a drag force which is dependent on their relative velocities? So the first e.o.m would look like ... = -kx1 - U(dx1/dt - dx2/dt) where the magnitude of the drag force is U times the relative speed. So, as if the blocks where on top of each other basically. How would we then construct a matrix as done at 6:20?

[@Galenus0]

Thank you, this was really helpful! :)

[@diedreikorper4736]

Thank you,it really helps! : )

[@atriagotler]

How can he write backwards that well😳

[@steveshaver4000]

Hi, Could you explain how specifying only the forces on both masses fully describes the kinematics and dynamics of the system? There is more than one position configuration for any set of forces for this problem, so specifying the forces alone cannot fully describe the system. Could you make a video that discusses the possibility of modifying the kinematic equation Delta(d) = vot + 1/2 at^2 Into a dynamic differential equation? Also, your system seems to have 2 origins. Would it be better to derive the equations of motion twice, from two different frames of reference?

[@swapnilholkar8251]

😇 thank u sir!!

[@haseebkhawaja1050]

Can you provide the GUI code for the simulation you performed. I have found the solution but how to graphically simulate it like you did especially extension and compression in springs

[@ProfJeffreyChasnov]

My GUI Matlab code can be found on Matlab Central. You can search under my name.

[@kaushikdr]

Why is the force of the leftmost spring on the leftmost mass -k(x_1)? The distance from the leftmost wall to the mass would be the (lengthofeverything - x_1), right?

[@ProfJeffreyChasnov]

Hooke's law is just the extension or compression of the spring from its equilibrium position.

[@alijoueizadeh2896]

Thank you.

[@shantipriya2905]

Sir what is MATALAB

[@shalomibk]

Thank you!

[@Lofr-Of-UET09]

Goood work sir

[@vijayvel1055]

What do you mean by normal modes?

[@ProfJeffreyChasnov]

Oscillatory motion with a single frequency.

[@챠챠-q1i]

love your video! thanks a lot!

[@shantipriya2905]

Sir u r exlent

[@Julia-xk3rs]

Thank you!

[@doremon2006]

What if the connecting force is electrostatic repulsion instead of a spring?

[@ProfJeffreyChasnov]

Then you use the appropriate force law.

[@doremon2006]

@@ProfJeffreyChasnov But if the distance between the oscillators is large enough, and the electric charge of the oscillators small enough, it can be approximated to a spring, right?

[@ProfJeffreyChasnov]

@@doremon2006 I don't think so. The spring force is assumed linear and can be attractive or repulsive. You said electrostatic repulsion, like a plus-plus-plus charge? It is an inverse square law and always repulsive.

[@doremon2006]

@@ProfJeffreyChasnov Then I will never be able to create a "stiffness matrix" for the electrostatic case (the general case, which can be attractive or repulsive) using the charges q1 and q2... ok, the problem is hard then, even numerically on Matlab.

[@doremon2006]

@@ProfJeffreyChasnov Anyway, thank you very much for your answers and for making me think more about the problem! I will find a solution for that simulation...

[@kanakalakshmiy7450]

for two coupled oscillator symmetric mode correspondence to frequency is A) zero B) infinity C) lower D) higher