Simple Harmonic Motion (Differential Equations)

[@1ucasvb]

Same here. My goodness, the amount of "so we pull out the solution out of a magical hat, and you can see it works!" crap that goes on with harmonic motion pisses me off. This is elegant and pretty straightforward.

[@CrazyGamer-xi8rf]

Ikr

[@madmaxx4178]

Yes after so many searches and asking teachers i finally found this wonderful video

[@KingsleyIjike]

Perfectly illustrated, broken down into the simplest bits of information, extremely helpful. Thanks so much for demystifying this!

[@brecoldyls]

It sounds like there are crickets in the background, it's very relaxing 🦗🎻

[@anzatzi]

This is the clearest exposition of this topic I have seen, and I have seen many! I'm hoping you cover phase angle in subsequent videos. Also, KA does not cover this topic. Thanks

[@aphiwemkhwanazi2041]

best simple explanation i can found

[@petertsirushkin2555]

Holy shit this video is magical. You saved my grade!

[@kelvinadimaswijaya9523]

Oh my god! this is so beautiful!!! thankyou

[@jasontse6]

i don't understand the part where you add the test function "X=e^rt" part

[@DonRonRaven]

Well the argumentation goes pretty much like this: since x is a variable that has at each point in time t a certain value you can describe its value for every moment in time by an euler function- because every number can be described by an euler function! Therefor you can substitute x by the expression e^rt with r being a constant needing to be specified!

[@Madvilllain]

Thanks Dave, this helped a lot.

[@EngineermanCullen]

Awesome video! Thank you!

[@autmanmansour6996]

Wonderfully, you made it simple! Thank you!

[@arifindobson]

Thank you very much, really ope up my brain like a canned sardine! Awesome

[@davidkippy101]

Okay, but how do you get rid of the complex part of the solution.

[@peterduveen5218]

My question as well.

[@Andre-ql2ei]

You can just ignore it

[@amirfadzil]

It doesnt exist don't worry 😂

[@bryanfuentes1452]

i is just a constant...you can combine all constants into single constant. Ex. When we integrate both sides of equation, that should result to two constants, one for each side, but it can combine into one.

[@Mornys]

Thing to note here is that A and B can be complex. To get the real solution you must specificly choose A and B to be complex conjugates of each other. E.g. A = c + di, B = c - di. Then A + B = 2c, which is real and A - B = 2di becomes real when you multiply it with the i that was outside the brackets.

[@tornikeonoprishvili5069]

You are awesome! keep it up dude :)

[@garyzhang5099]

thank you soooo much, much clear than mine stutter prof

[@beatrizdasilvaoliveira1642]

Thank you very much! You helped me a lot

[@sectrex]

At the latter part of your solution, where you represented the variables by A and B, what happened to the conplex number, í?

[@hilamary]

It's just kind of hidden inside the C1-C2. While its definitely there if you decompose the problem, it really doesn't matter since we are just choosing arbitrary constants. So just replace it with B. That's the huge benefit of Euler's formula. It lets you jump from complex to real plane.

[@Mornys]

He made a booboo there. Thing to note is that A and B can be complex. To get the real solution you must specificly choose A and B to be complex conjugates of each other. E.g. A = c + di, B = c - di. Then A + B = 2c, which is real and A - B = 2di becomes real when you multiply it with the i that was outside the brackets.

[@georgekakumbi6683]

nice presentation and helpful

[@irvanka]

thank you very much :) really helpfull

[@marktiba5432]

Thank you very much for your help.

[@jayashreechandru9608]

thanks for this wonderful explanation:)

[@BProgrammer]

Good and clear explaination

[@DonRonRaven]

An example for a simple number would go like this: 2=e^x with x being ln2!

[@nnamdichimaroke5795]

Can you solve one in which the differential equation does not equal zero but a constant

[@addy7464]

Thanks a lot mate

[@halo199393]

is that equation at 9.51 the equation of Motion for SHM?

[@franciscoaguero9028]

So B is comlex or not? how can you not explain that?

[@massoverdrive11]

how would you go about making a programme to solve these equations if anyone had any info it would be much obliged

[@anuragregmi790]

helped alot ... thank you

[@rugbywowsorted]

How would you go about finding A and B? I understand you need some initial conditions but what form would they come in, in a question? Excellent video by the way

[@readap427]

+George Initial conditions could include many parameters, but for a scenario like this, velocity and position are common initial conditions. A and B represent the amplitude of the oscillations of the mass on the spring. The approach to finding A and B would be similar to determining the highest point of a projectile's path based on its initial launch angle and velocity, except instead of gravity acting on the mass, in this situation the spring force is acting on the mass... but the spring force depends on the position of the mass... hence the second-order DiffEQ. If you're curious about some examples, check out Walter Lewin's Lectures of MIT Physics 8.03. The whole lecture set (More than 20 lectures) is really well done, but I think lectures 1 and 2 will address your question effectively.

[@Thomasesquire]

how would you solve a differential equation for an inverse cube force?

[@shaneguan2985]

Like the video, but the sound quality is a bit bad.

[@farhantanvir1036]

Really helpfull

[@kingofblood96]

Hey, maybe you know the form of the solution dE/dt=0 for the same case? i mean, i want to find the same answer parting of dE/dt=0 you know how?

[@zamzamali4842]

Thanks!

[@vaultvon2126]

thank you

[@alexschannel8883]

Since B must be i times some real number how can Bsin(wt) be a real function?

[@starhopper4587]

im curious as well :S

[@Mornys]

He made a booboo. A and B can be complex numbers and to get a real solution to the whole equation you must choose A and B so that they are not just complex, but also complex conjugates of each other. Then in the 1st term imaginary parts get substracted out and in the 2nd term they get multiplied out, i*i = -1.

[@RbtV92]

you forgot to add the "i" to the sin function during the last conversion.

[@evankheva5992]

Your not Khan.

[@lincolndexter9514]

You are correct. Khan is trash

[@planckbro1700]

based

[@ericshaker9377]

I think I love you

[@TonyJKFL]

gatosexo