Oscillation is characterized by the movement of a body around a fixed point. When a body moves through its vibrational cycle there is a change of energy from potential to kinetic and then back to potential. A pendulum has zero kinetic energy at its greatest displacement and has its lowest potential energy when it is moving at top speed. When at top speed, the forces acting upon the pendulum are in equilibrium, however, its momentum causes the pendulum to continue moving. Once it reaches its maximum displacement it has zero momentum, however, the force of gravity causes it to fall back. This type of motion is known as simple harmonic motion.
A body oscillates with simple harmonic motion if its acceleration around a fixed point is proportional to its distance from that point. Furthermore, the direction of the acceleration must always be towards that fixed point. The equation for simple harmonic motion is a = -k*x, where a is acceleration, x is the displacement and k is a constant; the negative sign shows that the acceleration is always in the opposite direction to the displacement.
Calculating the constant is quite complicated and depends on various properties of the oscillating system.
Bodies that display simple harmonic motion oscillate both around a fixed point and at a fixed time. The frequency of a body is measured in cycles per second or Hertz, while the amplitude of the motion is its maximum displacement. The time it takes for a body to complete one oscillation is called the period; a pendulum 9.78 inches long has a period of one second. This is found using the equation T = 2π√(l/g), where T is the time period; l the length of the pendulum and g is acceleration due to gravity.
Knowing how bodies vibrate is important in both science and engineering. Oscillation is most obviously useful in the accurate measurement of time, with pendulum and spring clocks having been superseded by incredibly accurate clocks which work by measuring the atomic vibrations of cesium and rubidium. According to ScienceMuseum.org, these atomic clocks are even more accurate than the rotation of the Earth and are used to keep time for the Global Positioning System.