Period
Forces and Motion

## Period

Glossary Definition for 16-19 ## Description

The period, or periodic time, of a periodic variation of a quantity is defined as the time interval between two successive repetitions. See figure 1.

Period is usually represented by the symbol T.

The period of the variation is related to its frequency, f, by

T = 1f Figure 1: The period of a periodically varying quantity may be measured between successive equivalent points on a plot of the quantity over time.

## Discussion

It is usually easy to measure a period directly if the corresponding frequency is very low. For example, the rotation of the Earth on its axis has a period of approximately 24 hours and we measure its period. But for motion where the period is of the order of a second, or less, then it is usually easier to measure the number of oscillations in a given time interval and calculate the frequency and hence the period. The frequency of vibration of a loud-speaker cone is of the order 103Hz and the number of times it vibrates in one second is typically measured, e.g. by using a laser beam reflected from its surface to determine its velocity.

seconds, s

s

## Other commonly used unit(s)

minutes, hours, days, years

## Mathematical expressions

• The period T of a periodic phenomenon is related to the frequency f by

T = 1f
• The period of a simple pendulum of lenght l, oscillating with small amplidutde is given by

T = 2π    l g
• The period of a mass m suspended from a spring of stiffness k is given by

T = 2π    m k

• Frequency

## In context

Historically, periodic motion has been the principal means of keeping time. The length of the year is related to the periodic motion of Earth around the Sun, and the length of the day to the periodic rotation of the Earth about its own axis. Pendulum clocks depend on the fact that, for small angles, the period of a pendulum is independent of the amplitude of its motion and can be adjusted by altering the pendulum’s length. For example, a pendulum that is 1 m long has a period of around 2 seconds. Many electronic watches use the vibration of a quartz crystal as the basis of timekeeping; the vibration frequency is just under 30 kHz, corresponding to a period of 30 μs.

###### Period
appears in the relation T^2 ∝ a^3 f=1/T