2. Damped Free Oscillators

MIT 8.03SC Physics III: Vibrations and Waves, Fall 2016
Instructor: Yen-Jie Lee

A more realistic physical system, a damped oscillator, is introduced in this lecture. Prof. Lee shows the mathematical solutions actually match the behavior of physical systems. He also does an in-class demo to compare damped and undamped oscillators.

License: Creative Commons BY-NC-SA

[akaikeshi]

My university professor gave the same course in 7 classes also from Georgi's book. I couldn't understand almost anything, even after I read the book and took notes.
I haven't had a real professor for around 2 years now. You're keeping me in love with physics. Thank you so much! You're amazing. I've managed to learn so much

[BlueRaja]

As others have mentioned, the math for θ_ at 44:23 is incorrect. It should be Re[e^-iωt] = cos(-ωt) = cos(ωt), meaning his "general" form should actually just be e^Γt/2 * cos(ωt). The rest of the equation involving sin() does not follow from anything he did previously.

The reason this happened was because the function he introduced as a potential solution, Z(t) = e^iαt, is *A* solution to the differential equation, but it is not THE general solution. In other words, it does not encompass all possible solutions. This is because the general solution to the simple harmonic motion equation (from the previous lecture) is A*cos(ωt) + B*sin(ωt) before initial condition constraints, while Ae^iωt = A*cos(ωt) + iA*sin(ωt) which only has one free term instead of two. Thus Ae^iωt does not encompass all possible solutions.

(He later "corrects" it by claiming you get the sin() term from linear combinations of e^iαt. While it's true that this justifies the use of sin() in the general solution to the overall differential equation, it still does not justify that particular choice for θ_(t). He's just doubling-down on his mistake)

[ahmedelmawrdy]

Thnaks a
you gave me another chance to study what i love but couldn't study before because of some financial issues.
you made me, belive more that the science is free for all to know and study!

[MsYurarus]

this is a very nice warm-up for my physics 3 course next semester, thank you, Professor Lee.

[chirantanmandal]

2:03 😂😂😂😂😂 It's a baseball bat professor... Some kinda rod

[tyh]

Thanks ! Professor LEE, it is really my luck to have the best teacher like you. Maybe human culture is passed along with good tutorials and insights you have been communicating.

[Alexweno]

52:00 Why the heck he takes the IMAGINARY PART for the negative theta, but the REAL PART for the positive?

[yermomLeslie]

He is missing a l in the denominator. 19:43

[tmsyou]

I might just be confused but shoudn't Re[exp(-iwt)]=cos(wt)? I know this wouldn't make much sense as a solution but mathematically isn't it correct?

[BUETisAim]

17:16 I can tell bros are going through a lot at the same time. Even I'm watching some parts several times to understand what actually just happened at that moment. 😅😥

[benlou]

At 37:55, shouldn't is be Re(the left hand side)=0? So he is missing the Re?

[KW-]

1:15:22 actually Energy (If I can call it like that) is conserved in a different manner, not in the form of T+U=E (T=Kinetic Emergy, U=Potential Emergy, E= Total Energy) but in the form: T+U - v•(δU/δv)= E, you have to add the velocity gradient of the potential Energy and multiply it by v). So you make E*=E+v(δU/δv) to rewrite the equation as T+U=E*, E* is not conserved because it depends on time. (Actually one defines an effective potential U* as U*=U-v•(δU/δv))

The potential U is defined to satisfy F=d/dt(δU/δv)-δU/δx. *You can find the proof in any classical mechanics book but if you want I prove it in a reply.

In this case U(x, v)=(-bv+kx)x/2

[jaimemorenovazquez]

In the underdumped case, is theta minus the real part of zeta minus? Why?

[MaheshSharma-folj]

Respected Sir,
At 16:32, The direction of torque must be inside the plane, so R vector should be pointed along the length of rod(opposite to what you did)
please clarify my doubts

[arenkhachatryan]

Can somebody tell me how to get p-sets for this course

[gabe-du]

I have something to add, the rotational inertia I, shouldn't it be (1/4)*m*l^2 ? the formula isI = m*r^2, and r is supposed to be (1/2)*l, right? so shouldn't it be (1/4)*m*l^2 instead of (1/3)*m*l^2 ?

[ramankumar-rlrl]

sir, please provide more lectures on all physics chapters thank you

[kevincardenas]

Is it correct to say "energy is not conserved"? I mean after all Energy is ALWAYS conserved. What could be happening is that for a driven oscillator and a dampened oscillator is that energy from the system gets transferred to the surroundings of the system (in this case the air I guess) Can someone correct me if I'm wrong please?

[robpatterson]

I just stumbled apon you! Awesome dude!

[rashmibajpai]

I have seen that the name mit only enhances my focus of watching video 😅😅