A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of $$\sqrt {{{3k} \over m}} ,$$ the ratio of the amplitude of steady state response to the static deflection of the spring is __________

A solid disc with radius a is connected to a spring at a point $$d$$ above the center of the disc. The other end of the spring is fixed to the vertical wall. The disc is free to roll without slipping on the ground. The mass of the disc is $$M$$ and the spring constant is $$K$$. The polar moment of inertia for the disc about its centre is $$J = {{M{a^2}} \over 2}$$

The natural frequency of this system in rad/s is given by

A single-degree-freedom spring mass system is subjected to a sinusoidal force of $$10$$ N amplitude and frequency $$\omega $$ along the axis of the spring. The stiffness of the spring is $$150$$N/m, damping factor is $$0.2$$ and the undamped natural frequency is $$10$$$$\omega $$. At steady state, the amplitude of vibration (in m) is approximately

Considering massless rigid rod and small oscillations, the natural frequency (in rad/s) of vibration of the system shown in the figure is