Masses and Springs @drpeyam

Uploaded November 2024 | Updated September 2026, 1 week ago

Masses and Springs

We derive the famous mass spring ode, which models the motion of a mass attached to a spring. This differential equation depends on the mass of the object, the damping constant of the spring (think friction) and the spring constant. It usually causes large oscillations and sometimes even damping and resonance. This derivation is based both on Newton's second law but also on Hooke's law. This is a must see for any aspiring mathematician and physicist, and gives a great application of second order differential equations

Subscribe to my channel: youtube.com/drpeyam
Instagram: instagram.com/peyamstagram
Teespring merch: dr-peyam.creator-spring.com/?

$life changing partial fractions trick$

$what is the plastic ratio? what is the plastic ratio? I define the plastic number and explain its properties, first as a cubic equation and a Fibonacci sequence to count bunnies, then as a fractal cube root with self similarities, and finally a cool formula with hyperbolic cosine function substitution. This is a cool journey through algebra, polynomials, inverse functions, and calculus. Proof that I did it before mathologer: https://youtu.be/SMeNVyJjd2o 0:00 Introduction 0:36 Fibonacci 1:45 Fractal 3:10 Hyperbolic trig Calculating hyperbolic trig functions: https://youtu.be/My2S-xbLPG0 YT channel: https://youtube.com/drpeyam TikTok channel: https://www.tiktok.com/@drpeyam Instagram: https://www.instagram.com/peyamstagram/ Twitter: https://twitter.com/drpeyam Teespring merch: https://teespring.com/stores/dr-peyam$ $solving a fractional differential equation$

$Inhomogeneous case Laplace transform and differential equations We use the Laplace transform to solve differential equations. The good news is that the same technique used to solve homogeneous ODE also works for inhomogeneous differential equations: Take the Laplace transform, solve for it, and then apply the partial fractions technique to find the inverse Laplace transform. This is a must-see for any mathematician, physicist, or engineer, enjoy! What is the Laplace transform: https://youtu.be/NmluV31oHq8 Laplace transform example: https://youtu.be/BHGnFcGhR5w Laplace transform playlist:https://www.youtube.com/playlist?list=PLJb1qAQIrmmB3NiV7Fy0tWcSmAYLQ7SCS Subscribe to my channel: https://youtube.com/drpeyam Instagram: https://www.instagram.com/peyamstagram/ Teespring merch: https://dr-peyam.creator-spring.com/?$