A single degree of freedom mass-spring - viscous damper system with mass $$m,$$ spring constant $$k$$ and viscous damping coefficient $$q$$ is critically damped. The correct relation among $$m, k$$ and $$q$$ is

The rod AB, of length 1 m, shown in the figure is connected to two sliders at each end through pins. The sliders can slide along QP and QR. If the velocity V_A of the slider at A is 2 m/s, the velocity of the midpoint of the rod at this instant is ___________ m/s.

The system shown in the figure consists of block A of mass 5 kg connected to a spring through a massless rope passing over pulley B of radius r and mass 20 kg. The spring constant k is 1500 N/m. If there is no slipping of the rope over the pulley, the natural frequency of the system is_____________ rad/s.

The heat removal rate from a refrigerated space and the power input to the compressor are $$7.2$$ $$kW$$ and $$1.8$$ $$kW$$, respectively. The coefficient of performance $$(COP)$$ of the refrigerator is ___________