# Period

The period, T, is the time it takes for an object to complete one entire oscillation. It is the reciprocal of the frequency and it has the unit of time (seconds in SI).

The period of the oscillation for a mass attached to a spring moving according to Simple Harmonic Motion can be derived from the equation of motion. It is the same whether the spring is horizontal or vertical and its expression is given by:

Where m is the mass and k is the spring constant.

The heavier the mass, the longer the time needed to complete one oscillation, so the longer the period and the smaller the frequency. The stiffer the spring, on the other hand, the shorter the period and the larger the frequency.

We see that the period (and the frequency) are characteristic of the specific mass-spring system (it depends on m and k). Each combination of masses and springs has its own characteristic period, which is independent of the amplitude of the oscillation. In other words, no matter how far from the equilibrium a mass is initially displaced, the period (and frequency) of the oscillation will stay the same (given the spring is also the same) and is given by the formula above.