Damped Harmonic Oscillators Derivation

[@tanmayvadhera4250]

I could not understand a thing during 2hrs of lectures. You explained almost everything in about 15 mins. Now, that's called teaching !
Thanks a lot!

[@lawliet2263]

10:22 how to go from step 2 to step 3? Can you do a detailed video on that and aslo i think it should be e to the power of negative something

[@LunaticPassport]

I am interested in that too.

[@salmaalfawal6155]

It's been hours of searching for what you have in your video
Thanks a lot

[@PhysicsThisWeek]

You are welcome.

[@DengPride]

I believe you missed a negative sign on line 2 on 10:24. It should be b*e^{-i*sqrt(w^2 - \gamma^2) *t}

[@shivangisoni2281]

Yes he missed it...

[@PhysicsThisWeek]

I did miss the negative sign. Thanks for catching that.

[@lel4159]

@@PhysicsThisWeek With the negative sign, can we still go from the 2nd line to the 3rd line that easily? I don't really see how that happens when both terms dont have a similar factor of e^isqrt(w²-phi2)t

[@PhysicsThisWeek]

@@lel4159 I'll be honest, imaginary numbers hurt my head. However, If you play around with some identities, you can show some intermediary steps where you get to e^(-γt) (a+b) cos( ω't)+(a-b)i sin ω't). Since these two terms are also solutions we can replace (a+b) and (a+b)i with two new constants c₁ and c₂. (I have to wave my hands why we then seem to ignore the i in c₂. Years ago I might have been able to explain it better, but I've been living in the real world.)
Then we can show that c₁ cos ω't + c₂ sin ω't can be written as A cos (ω't). (See math.stackexchange.com/questions/948329/how-is-a-sin-theta-b-cos-theta-c-sin-theta-phi-derived)

[@lel4159]

@@PhysicsThisWeek Thanks! Got it!

[@darrennixon8765]

My professor skipped a lot which you covered flawlessly. Thanks a lot

[@bablobko]

This is the best video on Damped Oscillation.

[@PhysicsThisWeek]

Thank you.

[@LunaticPassport]

Great video. I am interested in the math at (10:10 -10:20)available?

[@LunaticPassport]

Is it available anywhere?

[@cindychen1269]

Thank you very much! I eventually understood how the angular frequency comes from!

[@PhysicsThisWeek]

You are welcome.

[@little3960]

hi, is there a difference between the damping coefficient and the damping ratio, I still don't understand which is the damping coefficient from the equation

[@amiramduby]

This just made my life so much easier... Thank you so much!

[@muhammadwaqaraslam9451]

How b/2m=2 gamma sir can you tell me how you make this approximation

[@PhysicsThisWeek]

It isn't really an approximation, it is a substitution at about 5:10 in the video. It gives a better form to the equation. Later on, you use the correct form of beta. With the two in there, the auxiliary equation (around 5:58) has a "nicer" form.

[@muhammadwaqaraslam9451]

@@PhysicsThisWeek thanks sir

[@maleem5352]

very easy method
thanks

[@oldcoder9000]

Good video. Thanks

[@PhysicsThisWeek]

+oldcoder9000 I'm glad you liked it.

[@13Uzamakifan]

Subscribed!! Thank you so much, delivered all the essential info perfectly!

[@PhysicsThisWeek]

I glad you liked it. I hope it helps.

[@mavihs26]

So helpful thank you

[@shabanakhan2341]

Thank you very very much it was toooooooo much helpful for me.

[@muhammadwaqaraslam9451]

Sir love you 😘😘😘😘😘😘😘😘😘😘😘😘❤️❤️😜 you did a great work I was looking for this a so badly 💔

[@PhysicsThisWeek]

I'm glad it helped.

[@muhammadwaqaraslam9451]

@@PhysicsThisWeek sir can you tell me how you take b/2m=gamma

[@mem.j.8470]

Thank you very much 👍👍👍

[@Crookqt]

Thank you alot

[@stipepavic843]

thxxxx aloot :D !! subbed

[@lawliet2263]

This is how an American should sound like