Hi guys, Welcome to the Advanced Video Search Engine, and you are watching Undamped Mechanical Vibrations & Hooke's Law // Simple Harmonic Motion. That video is uploaded by Dr. Trefor Bazett at 2021-04-11T09:10:33-07:00. We are promoting this video only for entertainment and educational purpose only. So, I hope you like & enjoy it. [Z52emur7Rko]
| Name | Undamped Mechanical Vibrations & Hooke's Law // Simple Harmonic Motion |
| Video Uploader | Video From Dr. Trefor Bazett |
| Upload Date | This Video Uploaded At 11-04-2021 16:10:33 |
| Video Discription | MY DIFFERENTIAL EQUATIONS PLAYLIST: ►https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw Open Source (i.e free) ODE Textbook: ►http://web.uvic.ca/~tbazett/diffyqs Consider a mass on a spring moving horizontally. The only force on the mass is the spring itself which we can model using Hooke's Law. Then by Newton's Second Law that F=ma, this gives the differential equation mx''+kx=0. This is a second order, constant coefficient, homogeneous differential equation which we can study! We use our techniques from ODEs to solve this system and then do a bit of trigonometry to convert the answer to the standard form. This type of oscillation is often called either undamped mechanical vibrations or more generally simple harmonic motion as this occurs in a myriad of places in physics beyond just this scenario. 0:00 Mass on a Spring 1:18 Newton's 2nd Law & Hooke's Law 2:51 Solving the ODE 4:28 Rewriting into standard Form OTHER COURSE PLAYLISTS: ►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 ►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m ► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n ►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd ►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa ►LAPLACE TRANSFORM: https://www.youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 OTHER PLAYLISTS: ► Learning Math Series https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw ►Cool Math Series: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho BECOME A MEMBER: ►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett SOCIALS: ►Twitter (math based): http://twitter.com/treforbazett ►Instagram (photography based): http://instagram.com/treforphotography Z52emur7Rko |
| Category | Education |
| Tags | Solution | Example | math | harmonic motion | simple harmonic motion | mechanical vibration | frictionless | undamped | hooke's law | newton's law | laws of motion | differential equation | ODE | constant coefficints | oslve |
