\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\)

Period and Frequency

• The period and frequency of an oscillation are reciprocals of each other: $$T=\frac{1}{f} \qquad \hbox{AND} \qquad f=\frac{1}{T}$$
• Period is measured in units of time, like seconds. It may be useful to think of it as "seconds per cycle" in an oscillation. "It takes 4 seconds for the pendulum to complete one cycle" is a statement of period: $T=4\u{s}$
• Frequency is measured in units of "cycles per second", which is also known as Hertz (Hz). "The block on the spring completes 8 cycles in a second" is a statement of frequency: $f=8\u{Hz}$
• In the first example, the period is $T=4\u{s}$, so the frequency is $f=\frac1{T} = \frac14\u{Hz} = 0.25\u{Hz}$.
• In the second example, the frequency is $f=8\u{Hz}$, so the period is $T = \frac1{f} = 0.125\u{s}$.
• If the period is greater than one, the frequency will be less than one, and vice versa.