Answer
$k=\frac{[M]}{[T]^{2}}$
Work Step by Step
$T=2π\sqrt \frac{m}{k}$. Square both sides of the equation:
$T^{2}=4π^{2}\frac{m}{k}$. Now, solving for k:
$k=4π^{2}\frac{m}{T^{2}}$.
Dimension of mass: [M].
Dimension of T: [T].
$4π^{2}$ has no dimensions. So:
$k=\frac{[M]}{[T]^{2}}$
