DR. Vandiver, thank you for an awesome lecture of Linear System Modeling a Single Degree of Freedom Oscillator. The experiments and demonstrations are also fantastic.
My attempt: The natural frequency w is defined as the square root of the ratio of the terms before the variable (so k) and its second order derivate (so m). So for the linear equation, we get w=sqrt(k/m). The linear equation is a force equation, because all terms in that equation are forces. If we do the same for the rational equation, namely take the square root of the terms before the variable (the angle) and its second order derivate (the angular acceleration), we get the w you see there. The rotational equation is a moment equation; all terms in the equation are moments. We can make the transition from the linear to the rotational equation by multiplying by the radius (and vice versa) , because M = r X F. Therefore, when we calculate w for the rotational equation, r is in both terms and will disapper when we divide. Therefore, the expressions are equivalent. The term mLg is added, as the professor states, to account for the moment (per angle) provided by the small patch of material which was added under the collision. Likewise, the term mL^2 was added to account for the corresponding increase in intertial moment, or, equavalently, the moment per angular acceleration. With all this in mind, we can say that the natural frequency w is actually the square root of ( [the sum of the moments per angle] / [the sum of the moments per angular acceleration]) or, equivalently, the square root of ( [the sum of the forces per distance] / [the sum of the forces per linear acceleration])
+Stephen Goodman There are no required textbooks for this course, but suggested readings are drawn from the following texts: Hibbeler, Russell C. Engineering Mechanics: Dynamics. 12th ed. Prentice Hall, 2009. ISBN: 9780136077916. (www.amazon.com/exec/obidos/ASIN/0136077919/ref=nosim/mitopencourse-20) Williams, J. Fundamentals of Applied Dynamics. John Wiley & Sons, 1995. ISBN: 9780471109372. (www.amazon.com/exec/obidos/ASIN/0471109371/ref=nosim/mitopencourse-20) See the course on the MIT OpenCourseWare site for more details at: ocw.mit.edu/2-003SCF11
hi, i am interested to know is there any advantage of dealing in frequency domain while dealing with dynamics of continuous system? specially the catenary type structures (SCR)? if is there any what are they? any reference ? please help me in that
I think you are asking about the flashing light that has a variable frequency of the flashes. It is called a strobe light. You can also download a smartphone app to do the same thing.
This is just gold to mech students
better than my uc class
Parts of these lectures are actually useful to civil students as well, so gold for civil students as well I'd say.
Kim is a force of nature, these lectures are excellent.
DR. Vandiver, thank you for an awesome lecture of Linear System Modeling a Single Degree of Freedom Oscillator. The experiments and demonstrations are also fantastic.
Thank you! This is great content. The experiment helped visualize the dynamic amplification ratio really well
56:51 I presume he refereed to the book; S. RAO - MECHANICAL VIBRATIONS
Excuse me but why is the k for the bar bullet problem is
(M*g*L/2 + m*L*g)?at 30:56
My attempt:
The natural frequency w is defined as the square root of the ratio of the terms before the variable (so k) and its second order derivate (so m).
So for the linear equation, we get w=sqrt(k/m). The linear equation is a force equation, because all terms in that equation are forces.
If we do the same for the rational equation, namely take the square root of the terms before the variable (the angle) and its second order derivate (the angular acceleration), we get the w you see there.
The rotational equation is a moment equation; all terms in the equation are moments. We can make the transition from the linear to the rotational equation by multiplying by the radius (and vice versa) , because M = r X F.
Therefore, when we calculate w for the rotational equation, r is in both terms and will disapper when we divide. Therefore, the expressions are equivalent.
The term mLg is added, as the professor states, to account for the moment (per angle) provided by the small patch of material which was added under the collision.
Likewise, the term mL^2 was added to account for the corresponding increase in intertial moment, or, equavalently, the moment per angular acceleration.
With all this in mind, we can say that the natural frequency w is actually the square root of ( [the sum of the moments per angle] / [the sum of the moments per angular acceleration]) or, equivalently, the square root of ( [the sum of the forces per distance] / [the sum of the forces per linear acceleration])
Thank you. It's a really helpful and enjoyable lecture.
Thanks for this great lecture.
Many thanks
Any way that we can get the title of the text that was used that semester?
+Stephen Goodman There are no required textbooks for this course, but suggested readings are drawn from the following texts:
Hibbeler, Russell C. Engineering Mechanics: Dynamics. 12th ed. Prentice Hall, 2009. ISBN: 9780136077916. (www.amazon.com/exec/obidos/ASIN/0136077919/ref=nosim/mitopencourse-20) Williams, J. Fundamentals of Applied Dynamics. John Wiley & Sons, 1995. ISBN: 9780471109372. (www.amazon.com/exec/obidos/ASIN/0471109371/ref=nosim/mitopencourse-20)
See the course on the MIT OpenCourseWare site for more details at: ocw.mit.edu/2-003SCF11
Thanks
What about tutbomachinery
Absolutely well done and definitely keep it up!!! 👍👍👍👍👍
Really nice!
Quem precisa do RHAO agora?
Ss rao
Thank you sir！
hi,
i am interested to know is there any advantage of dealing in frequency domain while dealing with dynamics of continuous system? specially the catenary type structures (SCR)?
if is there any what are they? any reference ?
please help me in that
Chirag Palan yes
i am sorry but anyone know what is this device he was holding in his hands dealing with frequency? help plz
I think you are asking about the flashing light that has a variable frequency of the flashes. It is called a strobe light. You can also download a smartphone app to do the same thing.
ty very much man
*correction. It is also (more precisely) called a tachometer.
شباب في عرب هون عم يحضرو؟
Abdurahman Itani there's certainly some arab people but you should write in English language here!
Just try to be one like everyone here
Muhammed Al koussini يا هلا حبيبي من وين اخي انت؟مرحبا فيك نورت المكان
Muhammed Al شو مجالك بالهندسة؟
I am from Syria but i study a master of construction engineering in Germany
And you?
انا من لبنان :) بدرس هندسة ميكانيك في كندا
14:51
8.03 in 2 lectures minus EM waves
o_O
****