Frequency of S.H.M.

The frequency n of an S.H.M. is defined as the number of complete oscillations performed by the particle per unit time. Since, by definition of the period T, the particle performs exactly one complete oscillation in time T, it must perform $1/T$ oscillations in each unit of time. Hence

Combining this with the period formula $T = 2\pi\sqrt{m/k}$ from the previous subsection (for a spring-block system) gives the frequency written directly in terms of the force constant and the mass:

$n = \frac{1}{T} = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$ …