Скачать с ютуб Undamped Mechanical Vibrations & Hooke's Law // Simple Harmonic Motion в хорошем качестве

Undamped Mechanical Vibrations & Hooke's Law // Simple Harmonic Motion

MY DIFFERENTIAL EQUATIONS PLAYLIST: ►   • Ordinary Differential Equations (ODEs)   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:    • Discrete Math (Full Course: Sets, Log...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   ►CALCULUS I:    • Calculus I (Limits, Derivative, Integ...   ► CALCULUS II:    • Calculus II (Integration Methods, Ser...   ►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus ...   ►VECTOR CALCULUS (Calc IV)    • Calculus IV: Vector Calculus (Line In...   ►LAPLACE TRANSFORM:    • How to solve ODEs with infinite serie...   OTHER PLAYLISTS: ► Learning Math Series    • 5 Tips To Make Math Practice Problems...   ►Cool Math Series:    • Cool Math Series   BECOME A MEMBER: ►Join:    / @drtrefor   MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett SOCIALS: ►Twitter (math based):   / treforbazett   ►Instagram (photography based):   / treforphotography