A particle of mass $1\, {kg}$ is hanging from a spring of force constant $100\, {Nm}^{-1 .}$ The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period ${T}$. The time when the kinetic energy and potential energy of the system will become equal, is $\frac{{T}}{{x}}$. The value of ${x}$ is ..... .
JEE MAIN 2021, Diffcult
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${KE}={PE}$
${y}=\frac{{A}}{\sqrt{2}}={A} \sin \omega {t}$
${t}=\frac{{T}}{8}=\frac{{T}}{{x}}$
$x=8$
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