Episode 16: Harmonic Motion - The Mechanical Universe

Episode 16. Harmonic Motion: The music and mathematics of periodic motion.
“The Mechanical Universe,” is a critically-acclaimed series of 52 thirty-minute videos covering the basic topics of an introductory university physics course.
Each program in the series opens and closes with Caltech Professor David Goodstein providing philosophical, historical and often humorous insight into the subject at hand while lecturing to his freshman physics class. The series contains hundreds of computer animation segments, created by Dr. James F. Blinn, as the primary tool of instruction. Dynamic location footage and historical re-creations are also used to stress the fact that science is a human endeavor.
The series was originally produced as a broadcast telecourse in 1985 by Caltech and Intelecom, Inc. with program funding from the Annenberg/CPB Project.
The online version of the series is sponsored by the Information Science and Technology initiative at Caltech. ist.caltech.edu
©1985 California Institute of Technology, The Corporation for Community College Television, and The Annenberg/CPB Project

[@afonsodeportugal]

5:47 Graphic visualization of Hooke’s Law _F_ = -k. _x_ 13:15 Deduction of the differential equation that describes simple harmonic motion 14:32 Using a sine function with amplitude A and angular frequency _ω_ as a solution to the previous differential equation, i.e. _x_ = A.sin( _ω_ .t) 17:48 Visualization of the potential energy of the harmonic motion (bowl shaped curve) 25:02 Prof. Goodstein shows three examples of simple harmonic motion and discusses their importance in the context of stability

[@erictko85]

Wow. This is an incredible video. One of the best in the series. Thank you CalTech!

[@scienceinc.9453]

Prof. goodstein words adds greatly to the animated show.

[@brainstormingsharing1309]

Absolutely well done and definitely keep it up!!! 👍👍👍👍👍

[@clcmoreira2]

Thank you, Caltech!

[@bender7565]

This was on the PBS station in San Diego in 85-86. It was aired a year after I 'needed' all this stuff but it was great entertainment for me. A great find in the youtube vortex, good memories after 30+ years! Thanks!

[@jonathanfanning9558]

Wow, superb.

[@difusoseinfinitoslasidorem2241]

Bello por siempre..elegancia i simplicidad..fascinante..solo saber q estáis i ofrecéis a los amateurs..trabajos aterradores i puros de Genios ..q dedican sus Vidas a la Naturaleza..!!!!!!..bello FOREVER..ná vsigdá ..dlía vsiég..ná vsigdá !!!

[@universocalculado4639]

Pra quem não entendeu a parte que fala sobre os pêndulos oscilarem com a mesma frequência , independentemente de sua massa , eis aqui uma explicação : Vemos que sobre um pêndulo agem duas forças , a força T de tração , que o mantém preso a uma haste oscilando em um arco de círculo a uma distância fixa L e , a força da gravidade mg . Em seguida decompomos a força da gravidade em suas componentes horizontal que é igual força de tração ( T = mg cos a ) e vertical que é responsável pelo movimento ( F = - mg sen a ) , Assim , a força restaura o objeto para a posição de equilíbrio , mas o problema se torna mais difícil por tratar com uma função trigonométrica . Iremos então tomar um caso especial, a situação de pequenos ângulos ( sen a = a ) . Como a distância horizontal é x = L sen a , então para esse caso x = L a , e assim para a componente vertical escrevemos F = - ( mg / L ) x , comparando essa fórmula com a lei de Hooke ( F = - kx ) vemos que ( k = mg / L ) e finalmente substituímos na expressão da frequência . Se ( w = ( k / m ) ^ 1/2 ) então ( w = ( mg / mL ) ^ 1/2 ) ou ( w = ( g / L ) ^ 1/2 ) .

[@universocalculado4639]

Achei legal essa história do desenvolvimento dos relógios para melhorar a precisão na medição do tempo , pelo que entendi os primeiros relógios foram os relógios de Sol que , contavam o tempo muito bem exceto nos dias nublados , depois vieram os relógios de água que , também contavam o tempo muito bem até chegar o inverno e congelar a água , em seguida vieram os relógios de areia ( ampulhetas ) que , também contavam o tempo muito bem , mas se limitavam a contar pequenos intervalos de tempo , ainda vieram os primeiros relógios mecânicos mas não contavam o tempo muito bem já que a precisão dependia de cada relógio e por último vieram os relógios que utilizavam pêndulos para a marcação do tempo que , contavam o tempo muito bem , não se limitavam a contar pequenos intervalos e não dependiam do clima ou das estações .

[@leonsantamaria9845]

Despues los relojes, electronicos, supongo que los quanticos....

[@tovahkaplan9222]

a les miserables music 23:55 aladdin music 23:55 KSPS pbs summer 1994 11 16 2018 26:33 a 7th heaven movie river park square

[@cdrombrasil]

Simple harmonic motion is nature response to twanging any stable system. Its a bless of God.

[@goosew3266]

This is so annoying. Whoever put the Annenberg Media logo at the front of these videos really made a mistake. It throws the whole audio off the video. I have watched these lectures more than once, so I know there was not always this Annenberg Media introduction. Can someone please put it back to what it was?

[@pupdowg420]

You gotta feel it.

[@SalmanKhan-jn3zd]

The real understanding

[@SFKelvin]

"Simple Harmonic Motion is nature's response to twanging any stable system" #belomancy #StanfordCal #Russiagate #BachsCircleMozartsArrow

[@adolfninh23]

"In Western culture, few things govern the human life as steadily as the mechanistic concern with time". Epic phrase. Historian Oswald Spengler (author of Decline of the West) would definitely give it a like if he's still alive.

[@douglasstrother6584]

Get used to solving this problem in numerous contexts!

[@outofbox000]

6:57

[@outofbox000]

18:35

[@oker59]

they should have put the circle episode next to this one

[@abcdef2069]

caltech says it is not hooke who has invented the harmonic motion, but it was galieo. i guess the observation is not enough sometimes, you have to write it a math form.

[@pupdowg420]

Hahaha

[@421sap]

In Jesus' Name, Amen. God bless you ✨✝️

[@hiueasdasd7221]

MIT better than Caltech