A single degree of freedom spring-mass system of natural frequency $5 \mathrm{~Hz}$ is modified in the following manners:

Case 1 : Viscous damping with damping ratio $\varsigma=0.2$ is introduced in parallel to the spring. Case 2: The original undamped spring-mass system is moved to a surface with coefficient of friction, $\mu=0.01$. The ratio of the damped natural frequency for the cases 1 and 2 is given by____________ $\quad$ (in three decimal places).

A single degree of freedom spring-mass system of natural frequency $5 \mathrm{~Hz}$ is modified in the following manners:

Case 1 : Viscous damping with damping ratio $\varsigma=0.2$ is introduced in parallel to the spring. Case 2: The original undamped spring-mass system is moved to a surface with coefficient of friction, $\mu=0.01$. The ratio of the damped natural frequency for the cases 1 and 2 is given by____________ $\quad$ (in three decimal places).

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