A mass of 5kg is connected to a spring. The potential energy curve...

From the figure, $A = 2m$

$\dfrac{1}{2}m{\omega}^{2}{A}^{2} = 10$
$\dfrac{1}{2}m{\omega}^{2} ( 2{)}^{2} = 10$
$m{\omega}^{2} = 5$
$5\left({\omega}^{2}\right) = 5$
${\omega}^{2} = 1$
$\omega = 1$
$T = \dfrac{2\pi}{\omega} = 2\pi$
$2\pi\sqrt{\dfrac{ℓ}{{g}_{p}}} = 2\pi$
$2\pi\sqrt{\dfrac{4}{{g}_{p}}} = 2\pi$
${g}_{p} = 4m / {s}^{2}$