These systems can be mathematically described by using an elliptic integral to solve a second-order 
These systems can be mathematically described by using an elliptic integral to solve a second-order differential equation; those solutions are often simplified to a linear description by using Taylor expansion to replace the sine theta term with theta for small angles. The period of these systems can be approximated as two pi times the square root of length over gravitational acceleration. The double kind of these exhibits chaotic motion, and one of these used to demonstrate the rotation of the Earth was named for Foucault. For 10 points, name these physical systems used to model simple harmonic motion that consist of a mass connected to a string.
These systems can be mathematically described by using an elliptic integral to solve a second-order differential equation; those solutions are often simplified to a linear description by using Taylor expansion to replace the sine theta term with theta for small angles.
Pendulums [accept Pendula; prompt on Simple Harmonic Oscillators before "length"]