Periodic functions

Mechanical and electrical systems often involve periodic forces. A function $f$ is said to be periodic if there is a constant $p > 0$ such that

$$f(x + p) = f(x)$$ (3)

for all $x$. Any positive number $p$ with this property is called a period of $f$. For example, $f(x) = \cos x$ has periods $2 \pi, 4\pi$, etc. The smallest number $p > 0$ with the property (3), if it exists, is called the period, and the function is called "$p$-periodic", or "of period $p$".