When lift accelerates upwards, then effective acceleration on the pendulum

${\mathrm{g}}_{\mathrm{e}\mathrm{f}\mathrm{f}}=\mathrm{g}+\frac{\mathrm{g}}{3}=\frac{4\mathrm{g}}{3}$

$\therefore$ Time period $T^{\prime }=2\pi \sqrt{\frac{l}{{\mathrm{g}}_{\mathrm{e}\mathrm{f}\mathrm{f}}}}=2\mathrm{\pi }\sqrt{\frac{l}{4\mathrm{g}/3}}$

$=\frac{\sqrt{3}}{2}.2\mathrm{\pi }\sqrt{\frac{l}{\mathrm{g}}}$

$= \frac{\sqrt{3}}{2} T$