The fact that this video shot in 2004 is still prevalent and useful in 2021 shows that knowledge and dedication lives forever....great lecture sir.

@anishtaori1426

2 жыл бұрын

lundoi

@AJ-wq3xm

Жыл бұрын

Its going to be 2023 in some days these lectures are evergreen

@priyanshrawat442

8 ай бұрын

Damn i was born in 2004

@Vivir_Astucia

6 ай бұрын

U mean 2024

Sir I am from IIT. Even the professors here are really intelligent but they dont know how to impart knowledge to students. But you, are just awesome

@zombiesalad2722

4 жыл бұрын

Bhaiya aap quora use karte ho?

@waiitwhaat

3 жыл бұрын

fellow IIT-ian, and i 100% agree with you. This lecture helped me understand the concept so clearly, it's never getting out of my head again!

@dhruvpatel4773

2 жыл бұрын

Does this really comes in engineering!!! I am studying this for getting into IIT

@lecturesbywalterlewin.they9259

2 жыл бұрын

@@dhruvpatel4773 Keep in mind that MIT is only a very mediocre University. That's why only 101 people who studied at MIT or who lectured there received a Nobel Prize. *That's very embarrassing.* Luckily you got a much better education.

@dhruvpatel4773

2 жыл бұрын

@@lecturesbywalterlewin.they9259 oh sir.. you replied. But MIT is best university in world according to rankings. Even topper of NEET and JEE prefer MIT over other colleges. I don't know in dept about noble prices but 101 is very big number for me. I was socked to see your reply 🥴

I really enjoy watching your videos. I have learned so many things just watching about 20 of your lecture videos. May the cosmic force be with and God Bless you.

The real question is how he flawlessly did that dotted equilibrium line so quickly.

@lecturesbywalterlewin.they9259

6 жыл бұрын

kzread.info/dash/bejne/d4Frx5ubaK_Acps.html kzread.info/dash/bejne/eZyV2dmRk7TZhdY.html

@stephanielaughlin6790

6 жыл бұрын

Wasn't expecting an answer, amazing, thanks for sharing I'll check them out!

@kosmicviolet7540

4 жыл бұрын

@@lecturesbywalterlewin.they9259 This has turned into an addictive habit. Whenever I get to write on a chalkboard I always try to find a way to do this trick.

What a lovely way to enjoy Physics by watching your Lectures Professor Lewin, Kind regards.

This was really smooth. The pause button was my friend throughout this lecture. Thank you Professor. I felt so lost before. You've given me a new perspective on this.

@lecturesbywalterlewin.they9259

5 жыл бұрын

:)

Great sir. Today watching it for 25 timea but it's still feels amazing as if I am watching a movie....and not studying....long live professor.....

Thank you professor. The way you taught physics is fascinating.

Professor, around 54:00, you mentioned that an oscillation on that track, if there were 4 cars and 5 springs would have 4 resonance frequencies. It`s always the case when a system has n constituents that it will have n normal modes? Or the case is that it will have "up to n" normal modes? For example, if in that same track there were n cars and n+1 springs, and all the cars had different masses and the springs had different constants, would it still have, for sure, n resonance frequencies?

powerful enough to make physics enter my DNA. Fantabulous!

BEST Physics lecture I have never taken.

3:06 If the driving force was sin(wt), would the right hand side then have a factor of j?

How was the difference in the omega value(resonant frequency) calculated?

Thank you so much Professor, I am about to graduate in Acoustic Engineering and your lectures are a huge inspiration to think deeply about the basics of what I do. And obviously that is always crucial! Love from Italy ❤

@lecturesbywalterlewin.they9259

Жыл бұрын

you are very welcome

Brilliantly exciting. The on table demonstration-performance (43:50) is just about the best pedagogy I’ve ever seen.

@lecturesbywalterlewin.they9259

5 жыл бұрын

:)

@mp3lwgm

5 жыл бұрын

Live long and prosper.

What does the delta in the 1st proof stand for?

4:09 a reference for the future exams?

Wow, what an amazing professor! Thank you for this video!

Can someone please explain to me how could I get the Amax in 23:32 ? I tried substituting omega max into A but could not get the desired outcome.

Hi Walter, is it possible that the damping factor b is a complex number too?

Thanks, professor

apparently this is in the JEE Advanced syllabus now, and I've found this gem.....😅😅 Thank you so much sir!!

@vinayjumani839

4 ай бұрын

Yeah right 😅

What a wonderful full lecturer

What a fantastic professor

sir can you tell about instaneous power of the driven oscillators

Amazing lecture! thanks for sharing

@lecturesbywalterlewin.they9259

6 жыл бұрын

:)

Could you explain why the Amplitude, A=F(dot)/k when the frequency of the driving force tends to zero? When the direction of the driving force becomes constant(when the driving frequency tends to zero) does the equillibrium position shift?

@lecturesbywalterlewin.they9259

7 жыл бұрын

The answers are in my lecture

@gamerboyss5310

3 жыл бұрын

@@lecturesbywalterlewin.they9259 hahahaha

Thank you sir for your wonderful lectures

😍😍😍😍😘😘😘 falling in love is also a resonance and it can break your heart...👌👌👌👌👌

@lecturesbywalterlewin.they9259

5 жыл бұрын

very true

@learningdose7371

4 жыл бұрын

@@lecturesbywalterlewin.they9259 you killed it

At 3:20 shouldn’t cos(wt) = real part of (e^jwt) instead of just e^jwt?

i would like to your nice presentation but how cancel the sin and cos term

Nobel prize of best teacher goes to sir Walter lewin💞

This is very good. No wonder students have to pay a fortune to go there (if you are not bankrupt but show intelligence, or....). Most people will not realize how good this is, and actually think he is silly, or that it makes no sense at all. It's actually old knowledge explained clearly and efficiently. Americans are losing this to other places, but aren't even aware of it.

Is there still practice problem sets / homework assignments from 8.03 available online anywhere?

@lecturesbywalterlewin.they9259

6 жыл бұрын

homework assignments and exams of 8.03 are posted below the video thumb nails

@TrevorSchmahl

6 жыл бұрын

Thank you! I never noticed that before! Much appreciated.

Wow......... what a lecture it is!!!!!!! its more than awesome.......

@lecturesbywalterlewin.they9259

2 жыл бұрын

Thank you so much 😀

professor, for (3:40) you assert that the driver and driven frequency have to be the same as the "ultimate solution." (4:26) Is this "ultimate solution" referring to specifically the steady state solution? In that case, is the two equations that you have written down at (16:00) the steady state itself? I presume so. Essentially, are we uninterested in what initially happens to the system before it settles down? I know these are very obvious questions, but I just wanted to be absolutely sure. Also, is there a formula that tells you what happens before we let t go to infinity: like a general formula that tells you what the system is doing, and we can obtain the equations on the blackboard at (16:00) by taking the limit as t-> infinity?

@seanki98

7 жыл бұрын

we know it is steady state because you made the assumption that t->infinity the moment you wrote down that the angular frequency of the solution z has the same w as the driver, correct?

@lecturesbywalterlewin.they9259

7 жыл бұрын

The steady state solution of an oscillator driven with frequency omega will ALWAYS be omega.

Amazing prof

Prof Lewin, around @30:14 you said that eta is displacement "not a force", however, when your hand changes direction, there must be an acceleration due to the change in the direction of the velocity of your hand, in other words, the motion of your hand does exert a force on the object! Can you please clarify this for me, it is confusing

@lecturesbywalterlewin.they9259

5 жыл бұрын

I watched at 30:14. My lecture is x-tal clear, I cannot add to it.

Why, when assuming a a steady solution to the complex diff euqation, do we not assume that the amplitude (A) will be the same as the amplitude of the driving component (F0/m), just as we did with the frequency (w) ? Thanks in advance

@lecturesbywalterlewin.they9259

5 жыл бұрын

>>>will be the same as the amplitude of the driving component (F0/m)>>> how many minutes into the lecture?

43:00 the pendulum example, where we let the frequency go to infinity, could we say that the reason here that the phase difference goes to pi as effectively you have a "shorter" pendulum when performing the driven oscillations, and so it pivot about a point in the pendulum itself?

@lecturesbywalterlewin.they9259

7 жыл бұрын

if it helps you OK - it's not accurate though

At 10:44 ,Can the chosen frequency of the driven force be a initial condition in some sense?

@lecturesbywalterlewin.they9259

7 жыл бұрын

You can always choose a frequency, but your solution will then have a transient component which wil ultimately die out and after that you will have the steady state solution. .

walter lewin sir I need your help. 2:20 Your way of solving that differential equation is truly amazing. And I love that either. But while solving for the displacement x, I am trying to solve those using Laplace transform (In the past I used it and I got some weird terms along with original answer like the initial velocity term and sine and cosine in the same solution.). Would you recommend to use it?? Will it affect my solutions??

@lecturesbywalterlewin.they9259

2 жыл бұрын

talk my math with your math teacher

In the pendulum problem, we arrived at an expression for the periodic force acting on the pendulum. However, is there any other way of directly arriving at an expression for the periodic force?

@lecturesbywalterlewin.they9259

3 жыл бұрын

try it

Hi, I forgot what the Q was, I thought it was quality of the system but I must be mistaken cause when I looked it up I didn't find it. What is the Q? Thanks

@lecturesbywalterlewin.they9259

5 жыл бұрын

yes Q is called the "quality"

This man could teach a five year old this stuff and they would understand everything...

At 1.45 why we take external force as F=F°cos wt ?? I mean why didn't we use F=F° sin wt

@gamerboyss5310

3 жыл бұрын

because of the Euler expansion......cost+i.sint (basically to avoid complexity)

great video very informative and entertaining as well.

@lecturesbywalterlewin.they9259

3 жыл бұрын

Glad you enjoyed it!

I just fell in love with Walter Lewin! If you are a Physics Prof, watch this video. It's great, especially the ending.

@lecturesbywalterlewin.they9259

5 жыл бұрын

omg!

Sir how you write cos(wt)as a e^iwt. Because according to eulor e^iwt=cos(wt)+isin(wt)

@lecturesbywalterlewin.they9259

5 жыл бұрын

only the real part of e^iwt gives you the magnitude and that's the cos

Falling in love is a form of resonance and both can be destructive . വാക്കുകൾ അറം പറ്റി പോയല്ലോ ആശാനേ ;)

Regarding air track demo: In 8.01(lecture 31), you demonstrated the flipping of arrow (drive) at just above the resonance. but in this lecture's air tract demo, there is no such flipping. once omega is higher than omega zero, due to square root in amplitude equation, amplitude can be positive or negative. which value we have to prefer and on what basis we have to prefer. In 8.01(lecture 31), flipping occurs due to the negative values of amplitude above resonance frequency. can you shed some light in to this?

@lecturesbywalterlewin.they9259

7 жыл бұрын

how many minutes into the lecture?

@babuj6949

7 жыл бұрын

sir, in current lecture from 53.03 to 53.35 min, and in 8.01( lecture 31), from10.22 to 10.30 min

@lecturesbywalterlewin.they9259

7 жыл бұрын

you have to be a bit patient and wait till transient phenomena have died out. At 53:40 the two are perfectly out of phase. No need for me to look at 10:30.

Dear professor how do you know in advance ( with out any detail mathematical procedure) that the solution of differential equation must contain a delta term and this delta term must represent the phase difference between the driver and oscillator. Further more why the delta term is subtracted not added in the exponent ? thanks a lot for answering previous questions.

@lecturesbywalterlewin.they9259

7 жыл бұрын

The most general soln must contain a phase angle. Just like the most general soln for F=-kx must contain a phase angle. If you leave this out, in general you will not be able to meet the initial conditions.

really Amzing to watch....that kind of lecture although i have no interest in this subject and everything that pro.teachs is gone above my mind ........😥🤔🤔🤔🤔😍😍😍

Professor Lewin, please check your 8.03 playlist's lecture-3; it has been replaced by the third lecture of 8.03 posted by the "allure of physics" channel. Kindly, replace it with the original as the original one has better video quality. Thank you.

@lecturesbywalterlewin.they9259

4 жыл бұрын

I know this but I cannot fix it. On one day, out of the blue, I noticed that lect 3 of 8.03 was missing. I have no idea how that happened. Luckily I could link it to the version in "For the Allure of Physics".

Sir I am a fresher at IIT KANPUR and since our curriculum is similar to that at the MIT so your lectures are turning out to be of great use.THANKS A LOT SIR, The profs here are highly qualifier, they have abundance of knowledge but they lack the skills of teaching. I don't get that if IIT cannot provide profd who actually teach well then which institute can?????

Thanku, it made whole topic clear

Hello sir. I am wondering can the escapement within the metronome be considered as a driving force? And how can I model this movement of the escapement within the metronome?

@lecturesbywalterlewin.they9259

7 жыл бұрын

the metronome oscillates at its resonance freqs.

@jasonyu8995

7 жыл бұрын

yes, but their amplitudes are kept relatively the same as the starting amplitude. Originally they should very soon stop because of the damping, but now they can usually last for about 15minutes. Then the escapement must be driving the metronome from stopping no?

May I know the book you're using in your lecture about this topic ? I am a self tought

@lecturesbywalterlewin.they9259

2 жыл бұрын

8.01 Physics Hans C. Ohanian Physics Volume 1 2nd edition W.W. Norton & Company ISBN 0-393-95748-9 8.02 Physics for Scientists & Engineers by Douglas C. Giancoli. Prentice Hall Third Edition ISBN 0-13-021517-18 8.03 Vibrations and Waves by Anthony French CRC Press ISBN 9780748744473 8.03 Electromagnetic Vibrations, Waves and Radiation by Bekefi and Barrett. The MIT Press ISBN 0-262-52047-8 ---

I really don't understand why these students are not so participative in classes. Here in Brazil, at least, when the teacher has a good didactic, we always try to answer teacher's questions. In the video, they don't even help the teacher to correct silly mistakes (that can happen to everyone).

@lecturesbywalterlewin.they9259

7 жыл бұрын

same at MIT. I often ask questions like *who thinks it will increase? some students raise their hands * who thinks it will decrease? * who thinks it will stay the same I often ask questions that I want them to think about at home

@sn59826

5 жыл бұрын

They are simply dumbfounded by the brilliance of the lecture! I strongly wish that I had such teachers for all my subjects in high school and college. A proper understanding can ignite a person's creativity.

You can, in fact, break wineglasses with your voice! There's a catch, of course. The glass has to be made of crystal, and not amorphous glass. Crystalline glass has higher q compared to amorphous glass and can break cleanly. Mike Boyd demonstrated this in his video where he learned to do exactly this. kzread.info/dash/bejne/imqdrJKhgNOtlcY.html

Somebody knows how to obtain the pdf ? please

I want a lecture on damped oscillation but i am using a different book (waves & oscillations by M.H Musaddiq). What should i do? Its very different and difficult

@lecturesbywalterlewin.they9259

7 жыл бұрын

most college physics books cover this subject in the same way. 8.03 Vibrations and Waves by Anthony French CRC Press ISBN 9780748744473 8.03 Electromagnetic Vibrations, Waves and Radiation by Bekefi and Barrett. The MIT Press ISBN 0-262-52047-8

@ZoyaKhan-we8zi

7 жыл бұрын

thank you sir

The omlette on his shirt tho😂

Beste Professor Lewin. Ik heb een vraagje bij 25:13 , er is een nog omega met amplitude Q*F_0/k. Deze omega is lager dan omega_max. Behoort deze omega wellicht ook tot een vd eigenfrequenties?

@lecturesbywalterlewin.they9259

6 ай бұрын

ik gaf dit college in 2004 dat is 20 jaar gelend. Ik kan uw vraag daarom niet beantwoorden zonder ongeveer 20 minuten mijn video te bekijken en daar heb ik geen zin in. sorry - Ik kan U echter verzekeren dat ik geen fout heb gemaakt. groeten

Hi Mr.Lewin I really loved the video; it helped me understand a lot of things about resonance in the context of a pendulum. There was just one thing that didn’t make sense to me and that was why the amplitude formula (for a pendulum) showed that amplitude DECREASES as length INCREASES. This seemed to go against my intuition as I would have thought that the longer the pendulum, the greater the amplitude at different applied frequencies and especially at resonance. Why is my thinking wrong? Thank you - great video!

@lecturesbywalterlewin.they9259

5 жыл бұрын

how many minutes into the lecture?

@maxsamne3070

5 жыл бұрын

38:35 minutes in (when you slightly alter the amplitude formula to suit the pendulum). Thank you.

@lecturesbywalterlewin.they9259

5 жыл бұрын

I watched from 37:30 - 39:15 and I do not understand your question. *I then watched from **30:00** to **45:00** and I cannot add to the clarity of this lecture.* I suggest you watch it again

@maxsamne3070

5 жыл бұрын

Yes, it is more of an extension; I am writing a paper on how pendulum length impacts it’s amplitude during resonance. The equation shown at 38:37 suggests that as you increase the length of the pendulum (decrease omega zero), the amplitude, at resonance DECREASES. This didn’t seem to make sense for me, as I mentioned above, because I would have thought that increasing length, would increase pendulum amplitude (x distance from origin, x=0). Thank you

@maxsamne3070

5 жыл бұрын

Perhaps I can make my question simpler: what units is the pendulum Amplitude in (meters or degrees?) Thank you

Sir, wouldn't have a minus in the equation of tg of delta, or wouldn't be omega squared minus omega zero squared in the upstairs? (11:49). I've replicated the deduction and I checked in my book, and it does have, at least I that's what I think so.

@lecturesbywalterlewin.they9259

7 жыл бұрын

at 11:49 everything on the black board is correct.

@gugax10

7 жыл бұрын

Ohhhh, I've found my mistake. Thanks.

Sir at 1:04:44 , you mentioned that beat phenomenon occurs cause of same frequencies but in beat phenomenon frequencies should be different and amplitude should be same right?

@lecturesbywalterlewin.they9259

2 жыл бұрын

I watched at 1:04:44. Have you ever watched a movie where a car goes forward but the wheels rotate backwards? That's a beat phenomemon between the frequency of the images (1 image every 1/16 of a sec) and the motion of the wheel. I have a record palayer. It comes with a disc with black lines on it. You place the disk on the rotating table and you use flurescent light (fixed frequency 50 Hz or 60 Hz). You can now adjust the rotation speed of the turn table so that the black lines stand stil. *That too is a beat phenomenon.*

@pavankalyan-zi6ei

2 жыл бұрын

@@lecturesbywalterlewin.they9259 Not at all Intitutive 😅.

Hello, I have found this website on Richard Feynman's classes when he was teaching at CalTech : www.feynmanlectures.caltech.edu/info/ In the Exercise section, there is a problem dealing with the forced oscillation of a pendulum : www.feynmanlectures.caltech.edu/info/ When you look at the solution (winner of the Feynman Lectures Exercise Challenge), it is said : "Now we know from the problem that the system reaches a steady motion, and we argue that the steady motion, to be steady, has to be in phase with the sinusoidal motion of the pivot point that is forced to oscillate " This statement seems to contradict the fact that at the resonance frequency, the two signals should be out of phase with an angle of PI/2. Does anyone know what I could have missed out here? Thank you for your help. Best regards, JB

Thank you kindly ✍️

I have a question sir. At 00:03:05 the term was F/m cos(wt), we changed it to F/m e^(jwt). However isn't the expansion of e^(jwt)= cost(wt) + sin(wt)? How did we introduce the term sin(wt)?

@lecturesbywalterlewin.they9259

6 ай бұрын

changing to powers of e^j simplifies the math. At the end you only use the real term (thus the cos term)

@suhanipathak1689

6 ай бұрын

@@lecturesbywalterlewin.they9259 Okay sir, thank you.

Awesome 😀😀😊😊

Sir in my book it is given that maximum energy transfer takes place when system is in resonance,........so for a vibrating system in resonance must be having the largest amplitude.......so here we don't have maximum amplitude..,...why????

@shreyashmeshram5351

6 жыл бұрын

At 24 mins

thank you sir, you save me and show me the way to learn mechanical vibrations

@lecturesbywalterlewin.they9259

2 жыл бұрын

You are most welcome

What's the specific name given to Q

@lecturesbywalterlewin.they9259

6 жыл бұрын

quality

Sir, why did you write the differential equation of a linear motion and not of a circular motion?(pendulum problem)

@lecturesbywalterlewin.they9259

6 жыл бұрын

how many minutes into the lecture?

@tudorsechel5956

6 жыл бұрын

33:11

@lecturesbywalterlewin.they9259

6 жыл бұрын

it's not a circular motion

Sir at 3:01 why u replaced cos(wt) with e^wtj ...it should be e^wtj -sin(wt)j .....right???? Please tell where am I going wrong

@lecturesbywalterlewin.they9259

3 жыл бұрын

only the real part of Euler's eq counts!

@mohitvyas7727

3 жыл бұрын

@@lecturesbywalterlewin.they9259 Sir at 10.28 you wrote x= A cos(wt- delta) How we get that ? I can't understand it and sir why we use F=f° cos(wt) ?? I mean we can use F= f° sin wt

18:09 the 90° phase gap is actually obvious if one considers how resonances are physically created. Take a swing for example: when the swing comes to a halt, at that point the swinger is supposed to start pushing it

Sir, how do we interpret that when forcing frequency increases beyond resonance frequency, the amplitude becomes closer to F/(m*omega^2)?

@lecturesbywalterlewin.they9259

6 жыл бұрын

what do you mean by "interpret"? It follows from the differential eqs - I can't help it.

@mengkezhan3919

6 жыл бұрын

Thank you sir for the quick reply !!I was thinking if it is possible to 'visualise' it somehow like what you explained for the zero and infinite forcing frequency cases.

@lecturesbywalterlewin.they9259

6 жыл бұрын

Yes, I always try to make people as much as possible to see through the eqs. One way is to always apply expremes (e.g., like zero and infinity). The behavior that you addressed is not very easy to visualize. *Not all of Physics is.*

@mengkezhan3919

6 жыл бұрын

I see! Thank you sir!!:)

@lecturesbywalterlewin.they9259

6 жыл бұрын

try my bi-weekly problems! This one was my last Problem. I will post a new, VERY EASY one, later this week. kzread.info/dash/bejne/n5d2j6t8kampo9o.html

sir by euler's formula you have expressed cos(wt) as an exponential but that would also add a isin(wt) and wouldn't that be wrong . you've introduced it around 3.00 of the video

@lecturesbywalterlewin.they9259

4 жыл бұрын

yes e^(jwt)= cos(ωt) + jsin(ωt) I suggest you keep the sin term in your eqs. Near the end the result must be real and that's where you end up only with the cos term

@raghulsankar1153

4 жыл бұрын

@@lecturesbywalterlewin.they9259 ohhh . Thank you so much sir :D , I'll rework the whole thing !

very great explanation. but, i don't understand where did the -kx go in 34:25?

@lecturesbywalterlewin.they9259

Жыл бұрын

I cannot add to the clarity of this lecture

Thank you sir for such a awesome lecture ❤

@lecturesbywalterlewin.they9259

Жыл бұрын

Most welcome

Thnx prof.......

Sir what about if we get a so small Q that gives us an imaginary number making our wmax = wo*imaginary number for our highly overdamned system? What does it mean physically? Thanks in advance

@lecturesbywalterlewin.they9259

7 жыл бұрын

how many minutes into the lecture. Be specific, what becomes "imaginary'?

@ahmedcelik5448

7 жыл бұрын

At 22:14 you write the equation for wmax, but if the system is highly over damped Q will be very small and make the term under the square root a negative number. Therefore wmax=w0 times some imaginary number. What is the physical meaning then ?What does it represent? Thanks

@lecturesbywalterlewin.they9259

7 жыл бұрын

both terms under the sqrt are squared, Thus neither one can be negative.

@ahmedcelik5448

7 жыл бұрын

Yes of course but but if the term 1/2Q^2 is greater than 1 ;value of the (1-1/2Q^2) term will be negative and square root of it (sqrt(1-1/2Q^2)^1/2) will be imaginary

@lecturesbywalterlewin.they9259

7 жыл бұрын

You mentioned that w_max would become imaginary with highly overdamping. That is not the case. >>> if the term 1/2Q^2 is greater than 1 ; value of the (1-1/2Q^2) term will be negative and square root of it (sqrt(1-1/2Q^2)^1/2) will be imaginary how many minutes into the lecture?

EXCELLENT CLASS !!! THANK YOU SIR

@lecturesbywalterlewin.they9259

7 ай бұрын

You are very welcome

He is awsome

Sooo good

Sir i am little bit confuse in this lecture as well as in previous lecture , how exponential term is written in form of only cos , why not both cos and sin ?

@carultch

Жыл бұрын

You solve the differential equation in the form of the following. m*x" + k*x = 0 You start by making the assumption that x has the form of C*e^(r*t), where r is a constant that can be real or complex, and where C is an unknown constant. You'll get two solutions for r, and you then form a linear combination of the two. When you differentiate it at its various degrees, you get the following: (m*r^2 + k)*e^(r*t) = 0 You then solve a quadratic formula to get that r = +/- j*sqrt(k/m), which we'll call j*ω. Now you use Euler's formula to substitute back into the exponential function: e^(j*ω*t) = cos(ω*t) + j*sin(ω*t) And we construct a linear combination of both values of r: x = C1*e^(+j*ω*t) + C2*e^(-j*ω*t) By letting C1 and C2 be complex numbers, we can show that this is a linear combination of sine and cosine. Those complex numbers are: C1 = 1/2*(A - B*j) and C2 = 1/2*(A + B*j) Substitute C1 and C2 into the previous expression for x, and expand with Euler's formula. When we are finished, the complex coefficients will cancel, and we will be left with a linear combination of sine and cosine, where A and B are the respective amplitudes of the component functions: x = A*cos(ω*t) + B*sin(ω*t)

@carultch

Жыл бұрын

We can write x(t) in the form of a linear combination of two trig functions: x = A*cos(ω*t) + B*sin(ω*t) And we can also write it in the form of a single amplitude trig function and a phase offset: x = x0*cos(ω*t + φ) With trig identities, you can show how x0 and φ relate to A and B.

3:16 cos(wt) does NOT equal e^(iwt), where have the Im part of e^(iwt) has gone?

@lecturesbywalterlewin.they9259

5 жыл бұрын

we use a complex notation e^(iwt to solve the problem, but what matters at the end for the amplitude is the REAL part and that's the cos term

@tripp8833

5 жыл бұрын

@@lecturesbywalterlewin.they9259 you are a national treasure, Mr Lewin. My inspiration for majoring in physics!

Excellent lecture Sir 🙏🙏🙏

@lecturesbywalterlewin.they9259

2 жыл бұрын

Thanks

Whisch physicist has do do lot of work in vibration and simple harmonic motion

The delta Fn is signusoid Fn, it can be shifted to new equlibrium. For the soilder cannot across the bridge as they said respectfully, there is a story behind, if on foot soilder cross the bridge all at once if there is any acident by air or any then loss the unit otherwise just spill out or devide by half or smaller group also for far seeing.

@lecturesbywalterlewin.they9259

4 жыл бұрын

I mention this in my 8.01 lecture on resonance + Tacoma Bridge

Thanks you Sir

Professor, I have a doubt Driven force is written as F = fcos(wt) then could you please tell me what is f in the left-hand side of the equation my teacher told me that it's amplitude but we know F on the right-hand side of the equation is a "force" then f should be force according to the Law of homogeneity in dimensional analysis. Quantities of the same dimensions should be added, subtracted and equated. Being a trigonometric function cosine is dimensionless and F has a dimension of [M¹L¹T-²] and amplitude has dimension [L¹] .. Dimensionally equation is not correct The equation in dimensions: [M¹L¹T-²]≠ [L¹]

@lecturesbywalterlewin.they9259

4 жыл бұрын

F=fcos(wt) when cos is 1, then F = f when cos is --1, F=--f, when cos is zero, that F=0

Sir, why do you have some food item on right of your shirt in every lecture I see??

man i wish i found this in my first year of collage

I'll take mine sunny side up!

Sir I am from India and I liked Ur lecture very much So can u pls tell me which book u prefer to read

@mazbakamalratul3972

5 жыл бұрын

Vibration and waves A.p. frech

Nice lesson...what is Fo

can i please know how the phase varies with respect to change in Q

@lecturesbywalterlewin.they9259

7 жыл бұрын

follow my derivations that should answer your question. If I used Q somewhere, keep an eye on it.

@asifnawaz3146

7 жыл бұрын

your lecture was helpful in finding the phase equation, but I am not able to answer this question, can you please help me calculate the expression for the phase of the complex amplitude z(t)(which i already solved). Plot (qualitatively) the expression as a function of the driving frequency when Q → ∞, and Q ≠ 0 for the following cases: (z(t) is the solution to the driven, damped harmonic oscillator equation - model of the AFM tip). a) When Fsp = 0 b) When Fsp ≠ 0

@lecturesbywalterlewin.they9259

7 жыл бұрын

I looked briefly over my lecture and I cannot add to the clarity. Since this is covered in ALL college Physics books (solutions to 2nd order diff eqs),,I suggest you look elsewhere or ask google or ask quora.

@asifnawaz3146

7 жыл бұрын

i used the phase eqn from your lecture and deduced equation of phase in terms of Q viz. delta=arctan((Wo * W)/Q*(Wo-W^2))

@lecturesbywalterlewin.they9259

7 жыл бұрын

:)

Doctor, can the video be translated into Arabic? السلام عليكم