The figure below shows a planar mechanism with single degree of freedom. The instant center $${{\rm I}_{24}}$$ for the given configuration is located at a position.

A vibrating machine is isolated from the floor using springs. If the ratio of excitation frequency of vibration of machine to the natural frequency of the isolation system is equal to 0.5, the transmissibility ratio of isolation is

A uniform stiff rod of length $$300$$ $$mm$$ and having a weight of $$300$$ $$N$$ is pivoted at one end and connected to a spring at the other end. For keeping the rod vertical in a stable position the minimum value of spring constant $$K$$ needed is

A mass M, of 20 kg is attached to the free end of a steel cantilever beam of length 1000 mm having a cross-section of 25 $$\, \times \,$$ 25 mm. Assume the mass of the cantilever to be negligible and E_steel = 200 Gpa. If the lateral vibration of this system is critically damped using a viscous damper, the damping constant of the damper is