List of top Applied Mechanics and Design Questions on Vibrations asked in GATE ME

A 5 kg mass is suspended at the free end of an overhanging massless beam, having a pin support and a roller support, as shown in the figure below. Young's modulus of the material of the beam is 200 GPa and area moment of inertia of the beam is \(10^{-8}\) m\(^4\). The natural frequency of the beam in rad/s is

In a single degree of freedom vibrating system with only viscous damping, the critical damping coefficient is 350 N s/m and the damping coefficient is 35 N s/m.
The logarithmic decrement of the vibrating system is