Answer
$\frac{[M]}{[T]^{2}} $
Work Step by Step
$T = 2\pi\sqrt \frac{m}{k} $
$ \frac{m}{k} = (\frac{T}{2\pi})^{2} $
$ k = 4 \pi^{2} \times \frac{1}{T^{2}} \times m $
Dimensions of k = $ \frac{1}{[T]^{2}} \times [M] = \frac{[M]}{[T]^{2}} $
e.g. $kg/s^{2}$
