Coupled oscillators | Lecture 46 | Differential Equations for Engineers

Рет қаралды 101,261

5 жыл бұрын

Differential equations for two masses connected by three springs to walls.
Join me on Coursera: imp.i384100.net/mathematics-f...
Lecture notes at www.math.ust.hk/~machas/differ...
Paperback book at www.amazon.com/dp/B0BL9X4QWN/
Subscribe to my channel: kzfaq.info?...

Пікірлер: 68

@ProfJeffreyChasnov 4 жыл бұрын

Find other Differential Equations videos in my playlist kzfaq.info/sun/PLkZjai-2JcxlvaV9EUgtHj1KV7THMPw1w

@Saint_Studios 3 жыл бұрын

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

@rayquoiz5822 2 жыл бұрын

same

@dionysisevripidou2256 5 жыл бұрын

Best explanation i have seen. Thank you!

@karanpai9 3 жыл бұрын

Thank you for the great explanation!

@benvanhuyssteen4758 4 жыл бұрын

Thank you!! Brilliant simple explanation

@maxrybold1531 2 жыл бұрын

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.

@mathematicianjeff8358 3 жыл бұрын

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 2 жыл бұрын

kzfaq.info/get/bejne/la6kfbWYzr7aemg.html 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.

@salvatoremanfredid115 5 жыл бұрын

Amazing! Thanks

@user-vv4vx5tl5n 4 жыл бұрын

love your video! thanks a lot!

@datchentai3047 7 ай бұрын

Excellent presentation and explanation Thank you!

@diedreikorper4736 4 жыл бұрын

Thank you,it really helps! : )

@freemanfreed1581 3 жыл бұрын

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

@steveshaver4000 2 жыл бұрын

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?

@iamsosweetgahayah2977 5 жыл бұрын

Sir thank you

@swapnilholkar8251 4 жыл бұрын

😇 thank u sir!!

@Galenus0 5 жыл бұрын

Thank you, this was really helpful! :)

@TheTurkey72 4 жыл бұрын

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 4 жыл бұрын

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

@Julia-xk3rs 3 жыл бұрын

Thank you!

@janeknox3036 4 жыл бұрын

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 4 жыл бұрын

Haha! There must be some left-handed mathematicians!

@janeknox3036 4 жыл бұрын

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.

@rabbisadick6292 5 жыл бұрын

THE EXPLANATION IS VERY GOOG

@sashaguzman7792 Жыл бұрын

YOu're amazing, Thank you so much

@tianlouw8505 3 жыл бұрын

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?

@inzamamulhaq2310 2 жыл бұрын

Goood work sir

@alijoueizadeh2896 10 ай бұрын

Thank you.

@shantipriya2905 3 жыл бұрын

Sir u r exlent

@shantipriya2905 3 жыл бұрын

Sir what is MATALAB

@henrytu3720 3 жыл бұрын

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

@andersolofsson2841 8 ай бұрын

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.

@secularbanda1808 Жыл бұрын

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

@kaushikdr 4 жыл бұрын

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 4 жыл бұрын

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

@haseebkhawaja1050 Жыл бұрын

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 Жыл бұрын

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

@physicswalebaba1942 4 жыл бұрын

Sir love from india.😊

@user-si1zn3ir7x 3 жыл бұрын

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 3 жыл бұрын

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

@user-si1zn3ir7x 3 жыл бұрын

I got it thank you!

@goofi953 4 жыл бұрын

How did you create the Matlab simulation?

@ProfJeffreyChasnov 4 жыл бұрын

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

@salehalhumaid2078 4 жыл бұрын

how can I solve for random motion?

@ProfJeffreyChasnov 4 жыл бұрын

Using normal modes and random initial conditions.

@vijayvel1055 3 жыл бұрын

What do you mean by normal modes?

@ProfJeffreyChasnov 3 жыл бұрын

Oscillatory motion with a single frequency.

@doremon2006 3 жыл бұрын

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

@ProfJeffreyChasnov 3 жыл бұрын

Then you use the appropriate force law.

@doremon2006 3 жыл бұрын

@@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 3 жыл бұрын

@@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 3 жыл бұрын

@@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 3 жыл бұрын

@@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...

@swapnilholkar8251 4 жыл бұрын

I am from India 🇮🇳🇮🇳🇮🇳

@UseQPixinDune 4 жыл бұрын

No one cares

@HIMANSHUHARSHIT Жыл бұрын

padhhle bsdkkkkkkkkkk

@hasnnajm8345 Жыл бұрын

*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 ..