The damping ratio for a viscously damped spring mass system, governed by the relationship $$\,m{{{d^2}x} \over {d{t^2}}} + c{{dx} \over {dt}} + kx = f\left( t \right),\,\,\,$$ is given by

A mass $$m$$ is attached to two identical springs having spring constant $$k$$ as shown in the figure. The natural frequency of this single degree of freedom system 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.

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 _____________