
1. A single degree of freedom massspringviscous 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
(A) \(\large q=\sqrt{2km}\)
(B) \(\large q=2\sqrt{km}\)
(C) \(\large q=\sqrt{\frac{2k}{m}}\)
(D) \(\large q=2\sqrt{\frac{k}{m}}\)

2. 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.
3. 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.