Mechanical Vibrations: Underdamped vs Overdamped vs Critically Damped скачать в хорошем качестве

Mechanical Vibrations: Underdamped vs Overdamped vs Critically Damped

MY DIFFERENTIAL EQUATIONS PLAYLIST: ►   • Ordinary Differential Equations (ODEs)   Open Source (i.e free) ODE Textbook: ►http://web.uvic.ca/~tbazett/diffyqs In the previous video in the playlist we saw undamped harmonic motion such as in a spring that is moving horizontally on a frictionless surface just due to Hooke's law. In this video we upgrade and consider friction as well. We get a second order differential equation that is a constant coefficient homogeneous and we know how to solve these. However, qualitatively the type of solution you get depends on the constants. In the cast of underdamped, you get oscillations that decay exponentially. In the case of overdamped, that is too much friction, then it is just exponential decay with no oscillations possible. And then there is the very interesting third case of critically damped that gives a repeated root to the characteristic equation. ♡♡♡SUPPORT THE CHANNEL♡♡♡ ►Support on PATREON:   / drtrefor   ►MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett ►CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes 0:00 Deriving the ODE 1:58 Solving the ODE (three cases) 3:20 Underdamped Case 5:20 Graphing the Underdamped Case 7:33 Overdamped Case 8:50 Critically Damped COURSE PLAYLISTS: ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Logic, P...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   ►CALCULUS I:    • Calculus I (Limits, Derivative, Integrals)...   ►CALCULUS II:    • Calculus II (Integration Methods, Series, ...   ►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus (Vect...   ►VECTOR CALCULUS (Calc IV):    • Calculus IV: Vector Calculus (Line Integra...   ►DIFFERENTIAL EQUATIONS:    • Ordinary Differential Equations (ODEs)   ►LAPLACE TRANSFORM:    • Laplace Transforms and Solving ODEs   ►GAME THEORY:    • Game Theory   OTHER PLAYLISTS: ►Cool Math Series:    • Cool Math Series   ►Learning Math Series:    • 5 Tips To Make Math Practice Problems Actu...   ►LaTeX:    • Intro to LaTeX **Full Tutorial**  Part II ...   SOCIALS: ►X/Twitter: http://X.com/treforbazett ►TikTok:   / drtrefor   ►Instagram (photography based):   / treforphotography