The static deflection of a spring under gravity, when a mass of 1 kg is suspended from it, is 1 mm. Assume the acceleration due to gravity g =10 m/s² . The natural frequency of this spring-mass system (in rad/s) is _____________

A single degree of freedom spring mass system with viscous damping has a spring constant of 10 kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor (ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mm.

Which of the following statements are TRUE for damped vibrations?

$$P.$$ For a system having critical damping, the value of damping ratio is unity and system does not undergo a vibratory motion.
$$Q.$$ Logarithmic decrement method is used to determine the amount of damping in a physical system.
$$R.$$ In case of damping due to dry friction between moving surfaces resisting force of constant magnitude acts opposite to the relative motion.
$$S.$$ For the case of viscous damping, drag force is directly proportional to the square of relative velocity.

In a spring-mass system the mass is m and the spring constant is $$k$$. The critical damping coefficient of the system is $$0.1$$ kg/s. In another spring mass system, the mass is $$2m$$ and the spring constant is $$8k$$. The critical damping coefficient (in kg/s) of this system is __________