$$ $$ $$ $$ $$ $$ $$ $$ $$ $\text{Extra close brace or missing open brace}$ $\text{Extra close brace or missing open brace}$ $$

Period and Frequency

• The period and frequency of an oscillation are reciprocals of each other: $$T=\frac{1}{f}\text{AND}f=\frac{1}{T}$$
• 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: $T=4\mathrm{s}$
• 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: $f=8\mathrm{Hz}$
• In the first example, the period is $T=4\mathrm{s}$, so the frequency is $f=\frac{1}{T}=\frac{1}{4}\mathrm{Hz}=0.25\mathrm{Hz}$.
• In the second example, the frequency is $f=8\mathrm{Hz}$, so the period is $T=\frac{1}{f}=0.125\mathrm{s}$.
• If the period is greater than one, the frequency will be less than one, and vice versa.