TIME-DELAY OSCILLATOR AND INSTABILITY - A DEMONSTRATION

A harmonic oscillator where the force is dictated not by the current position but the position at a slightly earlier time is considered and shown to be unstable. This and closely related systems are called time-delay oscillators and the instability, when it is present, is called a time-delay instability. A simple, easy to construct demonstration is presented and analyzed. A discussion of the robust nature of the instability is also given.