Given that $\displaystyle{ \mathcal{L} \left\lbrace \frac{\cos\left(2\sqrt{3 t}\right)}{\sqrt{\pi t}} \right\rbrace = \frac{e^{-3/s}}{\sqrt{s}} }$, find the Laplace transform of $\displaystyle{\sqrt{\frac{t}{\pi}}\cos\left(2\sqrt{3 t}\right)}$. $\displaystyle{\mathcal{L}\left\lbrace\sqrt{\frac{t}{\pi}}\cos\left(2\sqrt{3 t}\right)\right\rbrace =}$