A particle of mass 1kg is hanging from a spring of force constant...

$KE = PE$
$\dfrac{1}{2}k\left({A}^{2} - {x}^{2}\right) = \dfrac{1}{2}k{x}^{2}$
${x}^{2} = \dfrac{{A}^{2}}{2}$
$x = \pm \dfrac{A}{\sqrt{2}}$
$y = Asin\omegat$

$\dfrac{A}{\sqrt{2}} = Asin\omegat$
$sin\dfrac{\pi}{4} = sin\omegat$
$\omegat = \dfrac{\pi}{4}; t = \dfrac{T}{8} .$ Thus $n = 8$