A particle of mass 1 kg is hanging from a spring of force constant $100 \mathrm{Nm}^{-1}$. 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 $\_\_\_\_$ .
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