Period and Frequency

The period of an oscillation, as mentioned before, is the time it takes to complete one cycle. It is represented by the variable $T$. The larger the period is, the longer it takes for the oscillation to complete one cycle.

Note

Capitalization is very important in physics, where we usually need more letters than are available in the alphabet. Thus, you should always use a capital $T$ for period, to avoid confusion with the lower-case $t$, which stands for time in general.

The period $T$ is usually measured in seconds, though its occasionally useful to think of this as "seconds per cycle" (s/cyc).

Example

If the period of an oscillation is 4s, how long does it take for it to complete 3 cycles? $$4\u{s\over cyc} \times 3\u{cyc} = 12 \u{s}$$

If it takes 4 seconds for an oscillator to undergo a cycle ($4\u{s\over cyc}$), then every second it undergoes a quarter of a cycle ($\frac14\u{cyc\over s}$). This latter quantity is called the frequency of the oscillation, and is the reciprocal of the period:

$$f=\frac{1}{T}$$

The units of frequency are cycles per second, but are more commonly known as Hertz (Hz). The larger the frequency of an oscillation, the faster it completes each cycle.