I've been studying Physics for 3 years and YET have I been able to find ANYONE that can explain this even remotely as clear as you have done. I am so absolutely grateful for this magnificent explanation.
Thank you!!!!! This is just the best. I've take two physics classes covering this problem and non have even come close to explaining it as clearly as this. Keep up the good work. Thanks again.
great video! Just wondering, I don't understand why you said in the video that the individual forces never change direction, only the net force. In the configuration you show in the video, should'nt F3 be exerted leftward? Because the spring number 3 is compressed, shouldn't it exert a repulsive force? In the same way, if x1 were to be negative, shouldn't F1 be exerted rightward?
I'm glad you liked the video. You ask a great question. What I mean by the forces never changing direction is is that the force of each individual spring on a mass always points in the same direction. This is true because all of the springs here are "extension springs". This means that the coils of the springs are initially together, but stretched apart when you build the configuration shown. That means that they are always stretched. For example, spring 3, causing force 3 is always pulling the mass on the right to the right. That's why I mentioned that the springs are "pre-stretched". You could build this configuration using "compression springs" that would always be compressed, forcing all of the forces in the diagram to change direction. In theory you could also build this from "ideal springs" that could be compressed or expanded. In practice, though, springs are generally either compression or expansion springs. If you built it with ideal springs, your statement is completely correct, and you would have to be a bit more careful with directions.
@PhysicsThisWeek How did you postulate that in non-equilibrium position, the stretched section would be of greater magnitude relative to the squished? What's the reasoning behind this? Awesome explanation of setting up the problem nevertheless! Thank you.
Within my setup diagram, the stretched parts are longer than the squished parts. This means that for F = k Δx, the larger Δx has a larger force. The reason I did this is because for my "real" system, there are three expansion springs. These are ones that would have the coils all together when unstretched. If they did get compressed to that point, they would bend or twist, causing the system to likely fail. If you had other types of springs, you'd have to be a little bit more careful, but the general principle would work.
@@PhysicsThisWeek Thank you! Also the fact that you used F2 twice, it's because the force on the two masses is caused by the same spring? Do you foresee any circumstance where these would be different, for the same extension? Perhaps, an inhomogeneous spring? Furthermore, for the non-equilibrium case, could you explain each force? This is my understanding, - F1 is a restoring force to the left because of extension of the leftmost spring. - Why does F3 point to the right if its due to compression of the rightmost spring which naturally would want to be restored to the left? - For the middle spring, as l2=l0+x2-x1, the extension of the spring by x2 is causing a restoring force to the left and likewise, compression by x1 is causing a restoring force to the right?
Thks for the excellent explaination of coupled oscillators. It seems no-one else have done this well. I just derived the harmonic osc equation & rederived it from a universal approach en.wikipedia.org/wiki/Harmonic_oscillator#Universal_oscillator_equation Now I hope to derive a pair of coupled of universal oscillators & then eventually a network of them. Thks again
I've been studying Physics for 3 years and YET have I been able to find ANYONE that can explain this even remotely as clear as you have done. I am so absolutely grateful for this magnificent explanation.
Thank you!!!!! This is just the best. I've take two physics classes covering this problem and non have even come close to explaining it as clearly as this. Keep up the good work. Thanks again.
great video! Just wondering, I don't understand why you said in the video that the individual forces never change direction, only the net force. In the configuration you show in the video, should'nt F3 be exerted leftward? Because the spring number 3 is compressed, shouldn't it exert a repulsive force? In the same way, if x1 were to be negative, shouldn't F1 be exerted rightward?
I'm glad you liked the video. You ask a great question.
What I mean by the forces never changing direction is is that the force of each individual spring on a mass always points in the same direction. This is true because all of the springs here are "extension springs". This means that the coils of the springs are initially together, but stretched apart when you build the configuration shown. That means that they are always stretched. For example, spring 3, causing force 3 is always pulling the mass on the right to the right. That's why I mentioned that the springs are "pre-stretched".
You could build this configuration using "compression springs" that would always be compressed, forcing all of the forces in the diagram to change direction.
In theory you could also build this from "ideal springs" that could be compressed or expanded. In practice, though, springs are generally either compression or expansion springs.
If you built it with ideal springs, your statement is completely correct, and you would have to be a bit more careful with directions.
@@PhysicsThisWeek thanks, I had never heard about this distinction !
Absolute beast explanation thanks!-Spent hours trying to figure this out lol
I'm glad it helped!
me too
@PhysicsThisWeek How did you postulate that in non-equilibrium position, the stretched section would be of greater magnitude relative to the squished? What's the reasoning behind this?
Awesome explanation of setting up the problem nevertheless! Thank you.
Within my setup diagram, the stretched parts are longer than the squished parts. This means that for F = k Δx, the larger Δx has a larger force. The reason I did this is because for my "real" system, there are three expansion springs. These are ones that would have the coils all together when unstretched. If they did get compressed to that point, they would bend or twist, causing the system to likely fail. If you had other types of springs, you'd have to be a little bit more careful, but the general principle would work.
@@PhysicsThisWeek Thank you! Also the fact that you used F2 twice, it's because the force on the two masses is caused by the same spring? Do you foresee any circumstance where these would be different, for the same extension? Perhaps, an inhomogeneous spring?
Furthermore, for the non-equilibrium case, could you explain each force? This is my understanding,
- F1 is a restoring force to the left because of extension of the leftmost spring.
- Why does F3 point to the right if its due to compression of the rightmost spring which naturally would want to be restored to the left?
- For the middle spring, as l2=l0+x2-x1, the extension of the spring by x2 is causing a restoring force to the left and likewise, compression by x1 is causing a restoring force to the right?
Best best explanation you have no idea how good this explanation is. No idea!
Definitely the best explanation. Regards from México.
Thanks. I'm glad you liked it.
PLEASE come out with part 2!
This has to be the best explanation right? I mean so many shitty videos I saw but this one is the godammn finest
Thank you.
@@PhysicsThisWeek r u kidding me sir? I should thank you, you don't know how much you helped me
The explanation was very clear. Thank you!
Very good explanation! Thank you.
Wonderful, Excellent!!!!!Plz make more videos.
Thxxxxxxxxxxxxxx a lot, this explanation of yours is the best for sure!
Wow! the video really helped.Thanks Sir.
Aradhana Bhattacharyya, You're welcome. I'm glad it helped.
Big up yourself brother👌👍
Very good !! Thank you very much !!
Thks for the excellent explaination of coupled oscillators. It seems no-one else have done this well.
I just derived the harmonic osc equation & rederived it from a universal approach
en.wikipedia.org/wiki/Harmonic_oscillator#Universal_oscillator_equation
Now I hope to derive a pair of coupled of universal oscillators & then eventually a network of them. Thks again
Love it! Thank you very much!
great video!!! thank you.
+crazyLocko You are welcome.
Coordinates*?
+Alex Drozd Thanks for catching that.
Thank you so much!!
+MayAlonMay , you are certainly welcome. I hope these help.
Thanks
so helpful, thank you :)
thank u somuch,really
helped
so good
thanks 🙏
Nice
Thank you alot aloooooooooot
You're welcome!
Wonderful, Excellent!!!!!Plz make more videos.