poles

4 videos across 3 channels

Poles are the critical points in the complex plane where a transform becomes unbounded, and they govern how systems respond over time. Through the Laplace transform, these poles reveal the exponential building blocks behind dynamics, determining decay rates, oscillations, and stability as you move from the time domain to the s-plane. The videos illustrate this intuition with geometric pictures, showing how exponentials map to simple poles and how poles shape both natural and forced responses in differential equations and engineering contexts.