A particle excutes $SHM$ on a straight line path. The amplitude of oscillation is $2\,cm$. When the displacement of the particle from the mean position is $1\,cm$, the numerical value of magnitude of acceleration is equal to the numerical value of magnitude of velocity. The frequency of $SHM$ is (in $second^{-1}$)
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$2\,\frac{{{d^2}x}}{{d{t^2}}} + 32x = 0$
where $x$ is the displacement from the mean position of rest. The period of its oscillation (in seconds) is