## Periodic and Oscillatory Movement

In the study of oscillatory movements are based some of the greatest advances in science, such as the first accurate measurement of the acceleration of gravity, scientific proof of the rotation of the earth, and numerous technological benefits, such as the invention of early mechanical clocks.

## Periodic motion

A periodic movement is characterized when the position, velocity and acceleration of a moving body are repeated at equal time intervals, such as the movement of the clock hands, from any point demarcated on a speeding bicycle rim. constant or even the movement made by the planets around the sun.

We call *movement period* (**T**) the length of time these cycles take to repeat. Thus, as a number of *( no) *of repetitions over a given time interval (

**Δt**), its period will be given by the expression:

How *no* is a dimensionless quantity, the period has unity equal to the unit of time. In SI, it is measured in **seconds**.

Beyond the period, in a periodic movement, it is considered a quantity called *frequency *(f), which corresponds to the number of repetitions of the movement (*no*) over a given time interval (Δt), ie:

Analyzing the units of the relation, the frequency is measured by the inverse of unit of time, that is 1 / s that receives the name of **hertz (Hz) **in SI.

Comparing the period and frequency equations, we can define the relationship between them as: