A pendulum is suspended in a lift and its period of oscillation when the lift is stationary is $T_0$. What must be the acceleration of the lift for the period of oscillation of the pendulum to be $T_0/2$ ?
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$\mathrm{T}_{0}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}}}$
$\frac{\mathrm{T}_{0}}{2}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}+\mathrm{a}}}$
$\frac{2 \pi \sqrt{\frac{\ell}{\mathrm{g}}}}{2}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}+\mathrm{a}}}$
$\frac{1}{4 g}=\frac{1}{g+a}$
$g+a=4 g$
$a=3 g$ upward
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