Spring Pendulum Simulink Tutorial Video

Take any spring and measure its un-stretched length, ℓ. Attach a mass to the end of the spring. Choose a mass so that the equilibrium length of the spring (i.e., the length of the spring when there is no motion) is about (1.33)ℓ. Secure the upper end of the spring to a fixed pivot point. Pull the mass straight down a little bit from its equilibrium, release it, and watch its motion. The mass moves up and down like a simple spring-mass system should. But after a little while, the angle the spring makes with the vertical starts to increase while the up-and-down (or in-and-out) motion decreases. It decreases until the spring swings laterally only, like a simple pendulum, essentially without in-and-out motion. Then the angle starts to decrease, and the in-and-out motion starts to appear again. The sequence of events repeats itself. WHY? This is a nonlinear phenomenon called Nonlinear Resonance! It cannot be predicted by linearizing the differential equations of motion for small amplitudes of motion. This phenomenon occurs in many dynamical systems, e.g., satellites, ships, airplanes, buildings, and machines. Every engineer should be aware of it! MatLab Simulink is used to analyze this dynamic system.