8.03 - Lect 1 - Periodic Phenomena, SHO, Complex Notation, Physical Pendulum

Periodic Phenomena (oscillations waves) - Simple Harmonic Oscillations - Complex Notation - Differential Equations - Physical Pendulum
Assignments Lecture 1, 2 and 3: freepdfhosting.com/63073d984e.pdf
Solutions Lecture 1, 2 and 3: freepdfhosting.com/58521402f3.pdf

[@benedictspinoza1025]

I find it fascinating that this lecture was recorded when i was 3 months old, and here i am indluging in the same material for my course 19 years later. Timeless content professor!

[@amrithranganarjun]

I've moved soo far in engineering. I wish i spent my time with your video's earlier! I've spent days trying to understand the concepts which you've taught in 8.01, 8.02 and 8.03 which could have been shortened. Loved it! Will recommend every high school kid!

[@lecturesbywalterlewin.they9259]

:)

[@diwakarsingh48]

Please can you send me link of 801 I can't find them

[@thienthanhtranoan6723]

@@diwakarsingh48 did you find it?

[@adityagupta2604]

@@diwakarsingh48 search at youtube " walter lewin 801"

[@piratesofphysics4100]

( : -)~

[@fl45hman]

So glad I've stumbled upon these lectures. If only my lecturers were anywhere near as good as you, Professor, my engineering studies would me so much easier. Your passion is inspiring!

[@lecturesbywalterlewin.they9259]

+Random Username Thank you!

[@IrfanKhan-ck9nr]

Never have I ever seen any teacher, teaching with this much of passion😭... By going through your lectures, anyone can fall in love with physics... Thank you sir for all your efforts❣️...

[@lecturesbywalterlewin.they9259]

interestedvideos.com/physics-youtube-channels/

[@QQuantum]

15 years later I thank you very much for this a lecture!!!! I hope you have a great life.

[@twosongs7396]

I so love such Teachers. Their passion is contagious. They are a Gift to Mankind.

[@Akash_Hegde]

THAT WAS ONE BRILLIANT LECTURE!!!!! I JUST CAN'T GET ENOUGH OF HIS LECTURES...

[@lecturesbywalterlewin.they9259]

:)

[@rk99688]

Damn Professor Nergis Mavalvala was in the audience she had no idea she will be part o the team that will discover Gravitational Waves twelve years later

[@gamerboyss5310]

Huh????

[@aishwarikmandal]

@@gamerboyss5310 professor nergis mavalvala was present in the lecture hall. She discovered gravitational waves 12 years after this lecture

[@lecturesbywalterlewin.they9259]

Nergis was co-discoverer. Prof Rai Weiss of MIT and Kip Thorne of Caltech + 1 more person shared the Nobel Prize for this magnificent discovery.

[@gamerboyss5310]

@@lecturesbywalterlewin.they9259 nice

[@sarveshkulkarni7526]

@@lecturesbywalterlewin.they9259 That person was professor Barry Barish. Why everyone keeps forgetting him?

[@laughstan7890]

Apart from being informative, these lectures are quite fun to watch. Thank you for such pieces of art Professor Lewin!!

[@AbhaySingh-gs7ss]

Its pretty mesmerizing the way you teach sir... And also you teach every fact without missing anything. Thank you sir!!

[@devil8761]

No one is like you sir You made me love physics Huge respect from an Indian🇮🇳

[@lindajoseph4212]

Respected Sir Your lectures have let me explore physics in a beautifully different manner. Thank you for bringing out the aptitude for physics in me. Keep doing what you do; many students owe you.

[@lecturesbywalterlewin.they9259]

:) 😊

[@jahanvisogun1558]

I m not in high school and your abilities to make one understand are out standing that I get all of them so well!

[@muhammadqaisarali]

Waaoo Sir.. "Aaaa man point one five" and body language....lovely

[@user-yc9tv5sw1g]

Thank you for your lectures. MIT lectures with you that is excellent to understand physics to demonstrate phenomenon.

[@MaheshSharma-dy6sq]

sir, you just enabled me to understand how nature and physics are so intimately linked . i am from india and i want to become the greatest physicist and make my country proud. thank you

[@lecturesbywalterlewin.they9259]

good luck!

[@MaheshSharma-dy6sq]

@@lecturesbywalterlewin.they9259 thank you very much sir

[@ryanmalik9607]

@@lecturesbywalterlewin.they9259 🤗 Love from India 🇮🇳

[@dhananjaisharma4590]

Dangerous lecture to watch with your headphones on xD :P

[@lecturesbywalterlewin.they9259]

:)

[@jahanvisogun1558]

These badges on your shirt different in every video are just lovely especially that egg one!

[@ashishkumarsharma1323]

I was just thinking of it haha

[@muneebhassan528]

Dear Sir , its the best lecture I have ever had . I wish I could have taken it earlier . ❤ you Sir .

[@bell8837]

The greatest Physics professor in the world! 👍

[@gousemohiuddin5475]

Great great great no words to appreciate my aim is to become even 1% like you.

[@weilam]

It's like I am addicting to watch your lectures, from 8.01, to 8.02x, and now 8.03... You saved me from the bland and bored lectures by my phy prof..!!!

[@aculisib]

Thank you Professor Lewin!!!

[@xyzywjwhsye]

Sir what an excellent lecture delivered by you!!!! Love from BITS PILANI, INDIA

[@ptyptypty3]

wow, well Dr Lewin... I've seen about 90 % of your 801 and 802 videos... and now I've started with your 803 lectures.. I have to tell you... I really enjoy ALL your videos.. they are all Good!!.. but what I really need to tell you is that THIS video is the BEST I have seen!!.. From beginning to end you have scripted the video PERFECTLY.. your chalkboard execution, your Demonstrations, your Interaction with the Students.. ALL OF IT was a Perfect Lecture Video!!!.. THANK YOU!!.. I found myself pausing the video and taking NOTES and doing calculations. I was totally involved as if I were a Student sitting in your lecture hall.... Congrats!!..

[@lecturesbywalterlewin.they9259]

thanks for your kind words

[@ShivanshTrisal]

Really professor, you gave a five minutes break in an 85 min lecture. In my high school days, my physics teacher lectured SHM ( it was the same topic in the video and little bit more) for more than 6 hours. *YES YES YES YES WITHOUT ANY BREAK*. I almost died on that day

[@juniormaemo6986]

Professor you lectures are super exciting. Big up.

[@emilia6067]

I wish there was enough lectures by Walter to last me a life time

[@anilmangawa4566]

sir todaye I firstly took your lecture. I realiz that there is no one in india who can teach like you. I will teach students like you sir thank you

[@vaishnavsnair4517]

no one except alakh pandey :)

[@mayukh3556]

I wonder how much patience you have to answer all the questions we ask

[@AKBARCLASSES]

I have written something before " Oscillation in relation is okay but frequency of that should be moderate ". During the lecture I thought that this is something which is matching here. Thanks sir for your efforts always. I can feel physics more because of you. love you. :)

[@hansrajc6184]

Life would have been so simpler if he would have been my instructor🌸🌸

[@junaidkhan6329]

I love you sir from pakistan...you devote your whole life for physicss

[@tandrew0ate]

Thank you very much, great lecture! In the pendulum experiment you’ve predicted time 20.17+-0.2s and got 20.52+-0.15s. If we take the first time with the higher bound and the second time with the lower one, we get 20.37s in both cases, so can we say that the outcome was actually within the bounds of the prediction and that the friction wasn’t the problem?

[@lecturesbywalterlewin.they9259]

predcited 20.17+-0.2s - observed 20.52+-0.15s is in very good agreement with the prediction.

[@tomtim5232]

I wish I had a teacher like you

[@matron9936]

32:30 trick question haha 😆 Amazing lecture!

[@ved7653]

You are truly amazing..❤️

[@dummycarrot1748]

One of my main reasons why I want to study at MIT,the professors’ teaching are simple,easy to understand and interesting.Maybe one day I hope I will be able to join Master program at MIT.

[@lecturesbywalterlewin.they9259]

apod.nasa.gov/apod/ap240510.html

[@vilivont4436]

Brillian lecture.

[@yishakabrham5002]

professor of the century !!!!!!!!!!!

[@mid7699]

I m doing the chapter on oscillations. This lecture trigged my imagination.

[@markitsche987]

Professor Lewin I hope you are doing well. I've been busy working (and trying to breath). Someday I'll be able to revisit your classes again.

[@user-rf7fz9ut4p]

Is it possible to speed up the ball by the energy of falling and using gravity to return to the place because of the acceleration, thank you

[@sanjanas4640]

Physics is experiments!!!!! but the way we're learning it in school it's just. .. Thank you so much sirr it helped a lott to understand the concept 🙏🙏🙏🙏

[@lecturesbywalterlewin.they9259]

You are most welcome

[@davidviper3482]

About the heat problem. Is it because length gets bigger when heated?

[@nisafajrinalfalah9893]

sir. you are greatest a physic teacher who i ever see. your explanation is beyond of equation. are there next series 8.04?

[@shreyasdoddamani4594]

8.04 is quantum mechanics

[@indiancitizen2787]

Very informative and excellent lecture . Thanks to you lewin sir

[@lecturesbywalterlewin.they9259]

You are most welcome

[@nazirhussain1622]

You are physics legend ❤

[@sarahkabbani5984]

Hello! I'm a current MIT student and love your lectures! I was able to ASE 8.01 because of them! For that, thank you so much. In fact, I'm considering taking the 8.03 ASE. Do you think the 8.03 curriculum has changed much since you've taught it?

[@lecturesbywalterlewin.they9259]

8.01, 02, 03, 04, 05, 06 cannot change very much who will be teaching 8.03?

[@mohammadhaseeb7392]

Sarah, how to get admission in MIT... Plz explain to me

[@mohammadhaseeb7392]

Sarah plz share how to get admission

[@Nitish_003]

I am understanding him little because I am Indian guy and here english is not spoken in such flow but physics practicle Really amaze me ..... I try to write my word in English so you all my English guy 👦 understand....may my words are proper 😇

[@sguzzygang]

This is amazing

[@akashpadhye]

Thank you sir for your help

[@junaidkhan6329]

Good... understable about periodic motion...

[@Dra60oN]

In 8.03. do you also use book "Physics" by Ohanian? I managed to get a pdf version of a book called 'Physics for scientists and engineers,9th edition' from Serway,Jewett and it seems like a very nice book and plus it's very similiar to your lectures.

[@lecturesbywalterlewin.they9259]

+Ivan Antunović I used Antony French's book and Bekefi and Barrett.

[@ratnasaxena4754]

Where you got this book

[@Jirayu.Kaewprateep]

If you notice the equation, we can generate gravity force in the circle shape like in the movie if we had enough radius and orbit velocity. # For signaling sometime we use inband, outband signal then for some telephone application need to add keypad sound. Or some ppl may have an extra wide frequency range or driving.

[@adforfun3675]

rofessor, are there any lectures that explain the mechanics of waves? Topics like particle velocity, string wave speed, transverse waves on a string, etc.? Please point me to those, since I heavily rely upon your incredible lectures for my interest in physics.😁

[@bird9]

Thank you dear prof! you are such a good prof, AMAZING!

[@lecturesbywalterlewin.they9259]

You're very welcome!

[@bird9]

@@lecturesbywalterlewin.they9259 Thank you ! 🤗

[@williambradley835]

What an honor it must’ve been to be a student of Walter Lewin. Like watching Michael Jordan teach kids how to shoot basketball. Thank you for your contribution to physics.

[@piratesofphysics4100]

This is absolutely gorgeous and mesmerizing lecture

[@lecturesbywalterlewin.they9259]

Glad you think so!

[@piratesofphysics4100]

@@lecturesbywalterlewin.they9259 I have passion for physics. Currently I'm in physics major in "Dhaka University" where the famous "Bose-Einstein condensation " was discovered by Professor Satyandranath Bose. There are now only a few good professors left. I wish I were in your University 20 years ago when you were young. When you had good days 😄. I have mad respect for you.

[@khadijakhalil3726]

prof i wanted to ask that can we hear the same frequency from the video as you heard phyiscally in the classroom?

[@user-rf7fz9ut4p]

Please tell me in which lecture the acceleration overcomes gravity,the example of a ball gaining speed due to the attraction of the earth?

[@yajatagarwal5809]

Hello sir can you please explain why does flag perform wave motion , what is the necessary restoring force on it in case of steady winds. I have been thinking about that for so long now . It was at 7:08

[@diwakarsingh48]

And for having water in less than 17 second just make one outlet half the size of other so that at bottle intersection there is a gap also at the base of vertically held bottle make a hold and volla we have filling at a much accelerate rate

[@pankajkumardubey2345]

Love from India sir. 🙏🙏🙏🙏🙏🙏🙏

[@alhusseinosama8832]

Professor Lewin, i Wonder if there's any subtitles available. Thanks for all the great work!

[@lecturesbywalterlewin.they9259]

there are no subtitles on 8.03

[@lecturesbywalterlewin.they9259]

There are subtitles for 8.01, 8.02, and for many talks. Click on cc. There are no subtitles for8.03

[@aswina5308]

Sir,when i was reading a book on physics by resnick and halliday it was mentioned that the velocity of the particle at equilibrium is the highest when it is undergoing a SHO. But there was no explanation on why is it so.Could you please tell me why?

[@lecturesbywalterlewin.they9259]

Release a pendulum at angle theta. Its highest speed is when theta is zero. That's its equilibrium position.

[@UseQPixinDune]

The total energy in a system undergoing SHM can be considered a constant in the absence of damping. The total energy is a combination of potential and kinetic energy, and the proportion of the total energy taken up by either kinetic or potential energy keeps changing. At the equilibrium position, the kinetic energy contributes all of the total energy, resulting in the highest velocity. The opposite is true when the object is at the extreme position, or when the displacement equals the amplitude, at that instant, all of the energy consists only of potential energy, giving an instantaneous velocity of 0.

[@nidhishsharma9703]

Professor, if we are not doing anything then is it periodic. I mean to say that the graph of our moyion is Y=0 Where x axis represents time and y represents displacement

[@Anupamtechnique]

Happy Teacher's Day from India.

[@surendrakverma555]

Excellent lecture Sir. Thanks 🙏🙏🙏🙏

[@lecturesbywalterlewin.they9259]

Most welcome

[@princegarg5328]

Sir, Is the period of oscillation a function of initial angular displacement in case of large oscillations (>20deg) in simple pendulum?

[@lecturesbywalterlewin.they9259]

what I derive in class are periods for small angles. In the case of a simple pendulum the periods at 1 degree or 10 degrees are the same within the accuarcy of my measurements. In French' book you can find the EXACT period for any angle; it's a series. Large angle periods can also be derived for physical pendulums - try to find them online.

[@akashbhalerao3494]

Thanks sit Love from india

[@and_rotate69]

how does he calculate the error in the Hoop predection?

[@alhusseinosama8832]

Professor Walter, After taking 8.01, 8.02, 8.03, i'm considering taking 8.04 & 8.05 but i don't know which courses should i take after those. i saw 8.286 "The Early universe" in MIT OCW, & saw 8.421+8.422 (Atomic and Optical Physics I,II), also saw 8.333+8.334 (Statistical Mechanics I,II). I noticed that 8.333+8.334 & 8.421+8.422 are Graduate courses not undergraduate so i was wondering if you can suggest me what to see next? Thanks in advance, btw i enjoyed your courses alot

[@lecturesbywalterlewin.they9259]

keep doing what you are doing

[@alhusseinosama8832]

so you think that i should go after 8.286 when i finish 8.05?

[@akashpadhye]

Sir, If we try to draw the graph for y=a sin^2 (wt) then we will get same graph as sine curve but it is shifted above the x-axis.so that object will oscillate between x=0 to x=a with mean position at x=a/2 and it's time period will be half. So this condition is same as that of SHM with shifted mean position. So why can't we consider it as SHM?

[@lecturesbywalterlewin.they9259]

sin^2 is not a solution to d2x/dt^2 + kx = 0. Thus it is NOT a SHM. sin 2wt would be a solution.

[@balakrishnan4886]

Professor, At 17:00, are you trying to say that x0=xcost(wt+phi)? but wrote it as xcos(wt+phi)?

[@BruinChang]

Sometimes periodicity makes me wander around the realm of so-called reincarnation of organisms. To my limited knowledge, substances can cycle, regenerate, and combine again to some complexity, except for energy. What if the soul is something like energy? Does that imply the non-periodicity of soul and incompleteness of reincarnation? Enough wandering, it is time back to the series of lectures of vibration and wave!

[@williambradley835]

This a a hot topic in theoretical physics. Sadly there is no verifiable information on the topic and it cannot be tested. Nothing is implied nor proven to be untrue as of now therefore this topic is nothing but a conversation to have with no scientific evidence involved. Since there is no evidence to disprove it, it is assumed to be a theoretical possibility. Maybe one day.

[@anushakulkarni5769]

thank you so much

[@kelsang18.]

What if the mass of spring is not so small or also almost equal to the mass hanging ?

[@lovelymemes9179]

@7:52 ☆Love is a periodic motion☆ Great example 😍😍😂😂

[@adforfun3675]

Professor, what was it that you aid was on the pipe at 48:51? Couldn't hear it properly. Was it "grid"? But what is meant by a grid? Also, did anyone come up with an explanation for the pipe producing 110 Hz just by heating and cooling?

[@gerardhilde01]

Because of the hot grit the tube becomes a chimney. Cold air enters the bottom while the hot air leaves at the top hence creating the tone.

[@jainamshah5549]

Wonderful lectures sir! Can you please explain how the tornado helps air flow more easily at 50:23?

[@lecturesbywalterlewin.they9259]

use google

[@SiddharthSingh-zd7ny]

@@lecturesbywalterlewin.they9259 Lmao

[@diwakarsingh48]

I have a explanation for the heated cylinder phenomenon and its i say similar to the bottle with water phenomenon and the hot gases tend to come out of the cylinder but at the same time cold gases neeed to go in and that happend in a way similar to the bottle experiment and due to this the air gets a wave like motion giving us the sound of I'm wrong I would be happy if someone could correct me

[@Madrid09514]

When I born then on that time he was recording lecture

[@yunusnourredin]

At 30:31, why did you multiply the error for your reaction time with square root of 2? Isn't your reaction time independent of the mass of the object ?

[@lecturesbywalterlewin.they9259]

sqrt of the ration of the 2 masses

[@yunusnourredin]

@@lecturesbywalterlewin.they9259 So if we assume m_2 = 10000*m_1 then the ratio is sqrt(10000)=100 and therefore the uncertainty of measurement is also 100*0.15s = + or - 15 seconds. But if you were to measure it, it would still take 0.15 second to react and not 15 seconds.

[@hridayamkrishnahore2964]

Sir If a light bulb blinks every 1 sec can we say that it is oscillating with 1 oscillation per second

[@sriya9016]

Sir at 1:12:42, the mass at P is not equal to the mass of the whole ring. but why is it taken that way??

[@_N0_0ne]

Thank you kindly ✍️

[@lecturesbywalterlewin.they9259]

You are very welcome

[@JaiPrakash-bk3uv]

Sir is there way to measure the value of force without using netwon law

[@manjnarana9189]

What is most fascinating thing in physics that is not in any other subjects

[@SoumilSahu]

what's this 26-100 you keep referring to?

[@lecturesbywalterlewin.they9259]

it's the lecture hall at MIT where I gave that lecture

[@ratnapatel8192]

@@lecturesbywalterlewin.they9259 why it's named as 26-100🤔 sir

[@yashbahl4334]

It just is, you cant be explaining every little thingy

[@studywithjosh5109]

What textbook are the assignments from? Could you provide a link if possible for the textbook? Thanks

[@lecturesbywalterlewin.they9259]

I have ni links 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

[@studywithjosh5109]

Lectures by Walter Lewin. They will make you ♥ Physics. Thank you for the swift response

[@ankeunruh7364]

theta double dot - I like it!

[@zahidali1270]

nice lectures

[@sayanbhakta2892]

Which book text book should I use??

[@kohlraushpost9686]

Bravo!

[@pallabbhattacharjee2685]

Love you sir

[@ShivanshTrisal]

Professor, how can we find the time period of a spring system oscillating like a simple pendulum. I mean like a simple pendulum is made to oscillate by displacing it by a angle *theta* .There is a spring in place of a string.

[@lecturesbywalterlewin.they9259]

it's a classic problem. use google

[@bjornsahlin]

Great video! On the topic of physical pendulums - if you fire a bullet horizontally into (embedding itself into) the lower end of a rod with lenght L that's hanging vertically with a frictionless pivot about the top end. The rod and the bullet both have mass M. How can I express the maximum angle that the rod-bullet pendulum will make with the vertical?

[@lecturesbywalterlewin.they9259]

+psynfel Since the pivot is frictionless mechanical energy is conserved IF I may ignore the heat produced by the bullet. But that is NOT the case. The impact of the bullet is a completely inelastic collision. In all inelastic collisions heat is produced, thus mechanical energy is not conserved. The bullet hits the rod at time t=0 and stops in the rod,. Angular momentum relative to the pivot point is conserved comparing the time (t=0) just before the hit and just after. Before the collision the angular momentum is only in the bullet, it is LMv where v is the speed of the bullet. Immediately after the collision the angular momentum is I_tot*omega. I_tot is the moment of inertia of the rod + the bullet. That allows you to calculate omega at time t=0 when the rod is still in vertical position. Thus you now know what at t=0 the KE of the system (rod + bullet) is; it is 0.5*I_tot*(omega)^2. You have to know, of course, how to calculate I_tot of the system (see below). For t>0 you can now use the conservation of energy: 0.5*I_tot*(omega)^2= the PE when the pendulum (+ bullet) come to a halt at angle @. I of the bullet alone is M*L^2. The integral to calculate I of the rod alone is not very hard. The mass, dm, in a section dx of the rod is (dx/L)M. Thus the dI of section dx alone is (dx/L)M*x^2. Since you have to take all values of x into account, you have to integrate from x=0 to x=L. The integral x^2.dx is (1/3)*x^3 thus integrating between x=0 and L leads to (1/3)*L^3. Thus the I of the rod alone is (1/3)*M*L^2 and I_tot=M*L^2+(1/3)*M*L^2. The PE of the bullet alone is MgL(1-cos@). The PE of the rod alone (when the angle is @) of section dx is (dx/L)M*gh. h here is x(1-cos@). Since you have to take all values of x into account, you have to integrate from x=0 to x=L. The integral of x.dx is 0.5x^2. Since x goes from 0 to L, the integral becomes 0.5*L^2. Thus the PE of the rod alone is 0.5MgL(1-cos@). Using the conservation of energy at t>0 we find that 0.5*I_tot*omega^2=[MgL+0.5MgL](1-cos@). This is one equation with @ as unknown. Thus you can now find @ which is the angle when the rod and bullet come to a halt. You can now also calculate how much energy was lost in heat. Before the impact the total energy was 0.5*Mv^2 (v being the speed of the bullet). Just after the collision the total energy is 0.5*I_tot*omega^2. Thus the heat loss is 0.5*Mv^2 - 0.5*I_tot*omega^2. I suggest that you calculate which fraction of the total KE of the bullet is converted to heat. Let me know your answer please.

[@bjornsahlin]

+Lectures by Walter Lewin. They will make you ♥ Physics. Thanks once again for your amazing support on this one! I've been sitting for a couple of hours going and what I come up with is that @=arccos(1-((4v^2)/(9gL))). All I could think of was to use the relationship with v=omega*r and replace omega^2 with (v/L)^2. I'm not sure if that's even the right thing to do here.. And with the same substitution I got that the energy loss should be equal to (-1/6)mv^2. My eyes are bleeding and I'm not even sure if I'm on the right track here haha! That omega=v/r relationship can be used when there's a uniform circular motion which this cannot be treated as. Maybe in the instant when t>0 it can be applied. If not - I'm clueless!

[@lecturesbywalterlewin.they9259]

+psynfel PSYNFEL: v=omega*r is of NO relevance here. It's an equation that you remember without an appreciation for it's meaning. what is v and what r in your equation. If r is L your v would be the speed of the tip of †he pendulum which changes in time from a max value †o zero when the pendulum comes to a halt. Your v is NOT constant. V of the bullet is the speed of the bullet before hitting the pendulum; that's a given. That V will certainly show up in the value if @.. If that V is zero @ must be zero, if that V goes up, @ must increase. By using v=omega*r you are indicating that you are not yet ready to deal with these problems. Your time may come, but not yet. Apart from that I asked you to derive which fraction of the original energy in the bullet is converted to heat. I will derive that today for you and post it. I will also solve my equations for @. Using v=omega*r is as useless as using F=Ma as neither of these 2 equations are of any use here. Do not feel bad. You are learning!

[@bjornsahlin]

+Lectures by Walter Lewin. They will make you ♥ Physics. That's what I suspected. But I ran out of ideas :( Omega must be zero when @ is reached. Thank you for doing this Walter, it is very appreciated! I'm trying to figure this one out - I'll post if I think I'm on the right track.

[@lecturesbywalterlewin.they9259]

+psynfel alpha can be derived from my equations. Notice that I wrote, this is one equation with one unknown @. Thus you can solve for @. I will do that later today for you. I also derived the heat loss (call it H) in this inelastic collision. The FRACTION of the original energy that is converted to heat is thus H/(KE of the bullet). I will also calculate that and post it here.

[@bhattharshil1683]

Love from India इंडिया 🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳

[@subhankarpaira8662]

Sir ,what is the best textbook on wave and vibration which gives more concept. It's a honour to hear something from you

[@lecturesbywalterlewin.they9259]

Berkeley Book (I forgot the title)

[@subhankarpaira8662]

@@lecturesbywalterlewin.they9259 sir, is it from Berkeley physics course series "Waves by Frank S. Crawford, Jr.