Dimension of Spring Force Constant

Theorem
The dimension of a spring force constant is $\mathsf {M T}^{-2}$.

Proof
From Hooke's Law, we have:


 * $\mathbf F = -k \mathbf x$

where:
 * $\mathbf F$ is a force, of dimension $\mathsf {M L T}^{-2}$
 * $k$ is the spring force constant
 * $\mathbf x$ is a displacement, of dimension $\mathsf L$.

Let the dimension of $k$ be $D$.

Then we have:
 * $\mathsf {M L T}^{-2} = D \mathsf L$

from which the result follows immediately:
 * $D = \mathsf {M T}^{-2}$