To start the blog off— here is a quick video of a homemade toy, more of a kinetic sculpture, described by the phenomena of a coupled harmonic oscillator.
This objet d'art is comprised of a bent spring with one end attached to a phosphorescent bead and the other attached to a heavy, stable base. With the spring bent, the end of the spring has two points of pivot for swinging motion to occur, one swinging motion nearly perpendicular to the other. The interesting thing about how this spring was bent is that both modes of swing oscillate at nearly the same rate. In other words the two modes have the same frequency of oscillation. When this is the case the energy of the system will transfer back and forth from one motion to the other. Note the peculiar motion of the glowing bead. The ellipse-like motion arises from the combined swinging motions along the two directions and is described mathematically by a type of Lissajous figure.
That such an elegant and repeatable pattern can emerge from such a simple system still stirs in me a sense of surprise and wonder. This is the essence of the Physics Toy.