A simple pendulum 50 cm long is suspended from the roof of a cart accelerating in the horizontal direction with constant acceleration $\sqrt{3}\mathrm{gm}/{\mathrm{s}}^2$. The period of small oscillations of the pendulum about its equilibrium position (in seconds) $\left(\mathrm{g}={\mathrm{\pi }}^2\mathrm{m}/{\mathrm{s}}^2\right)$ is ___________.

With respect to the cart, equilibrium position of the pendulum is shown. If displaced by small angle $\mathrm{\theta }$ from this position, then it will execute SHM about this equilibrium position, time period of which is given by 

$\begin{array}{l}\mathrm{T}=2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{{\mathrm{g}}_{\mathrm{eff}}}}\text{ where }{\mathrm{g}}_{\mathrm{eff}}=\sqrt{{\mathrm{g}}^2+(\sqrt{3\mathrm{g}}{)}^2}=2\mathrm{g}\\ \Rightarrow \mathrm{T}=1.0\mathrm{s}\end{array}$