List the dimensions of each variable.

• Time period $T$: $[T]$
• Mass $m$: $[M]$
• Force $F$: $[M][L][T]^{-2}$ (since force = mass $\times$ acceleration)
• Distance $x$: $[L]$
• The constant $2\pi$ is dimensionless.

The LHS is $T$, so its dimension is $[T]$.

The RHS is $2\pi \sqrt{\frac{m}{Fx}}$. We only need to consider the dimensions of the terms under the square root.
Dimensions of $\frac{m}{Fx}$:

Now, take the square root of this expression:

So, the dimension of the RHS is $[L]^{-1}[T]$.

LHS dimension: $[T]$
RHS dimension: $[L]^{-1}[T]$
Since $[T] \neq [L]^{-1}[T]$, the formula is dimensionally incorrect.

The formula $T = 2\pi \sqrt{\frac{m}{Fx}}$ is dimensionally incorrect.