Differential Equations of Motion

Flash and JavaScript are required for this feature.

Download the video from iTunes U or the Internet Archive.

These equations have 2nd derivatives because acceleration is in Newton's Law F = ma
The key model equation is (second derivative) y ' ' = MINUS y or y ' ' =  MINUS a^2 y

There are two solutions since the equation is second order.  They are SINE and COSINE
y =  sin (at)  and y = cos (at)    Two derivatives bring back sine and cosine with minus a^2

The next step allows damping (first derivative)  as in my ' ' +  dy ' + ky = 0   How to solve?
Just try y = e^at   !!  You find that   ma^2 + da + k = 0   Two a's give two solutions: good

Professor Strang's Calculus textbook (1st edition, 1991) is freely available here.

Subtitles are provided through the generous assistance of Jimmy Ren.
 

Related Resources

Lecture summary and Practice problems (PDF)

Free Downloads

Video


Caption

  • English-US (SRT)