For a certain engine having an average speed of $$1200$$ rpm, a flywheel approximated as a solid disc, is required for keeping the fluctuation of speed within $$2$$% about the average speed. The fluctuation of kinetic energy per cycle is found to be $$2$$kJ. What is the least possible mass of the flywheel if its diameter is not exceed $$1$$ m?

A flexible rotor-shaft system comprises of a $$10kg$$ rotor disc placed in the middle of a mass-less shaft of diameter $$30$$ $$mm$$ and length $$500mm$$ between bearings (shaft is being taken mass-less as the equivalent mass of the shaft is included in the rotor mass) mounted at the ends. The bearings are assumed to simulate simply supported boundary conditions. The shaft is made of steel for which the value of $$E$$ is $$\,2.1\, \times \,{10^{11}}\,$$. Pa. What is the critical speed of rotation of the shaft?

A uniform rigid slender bar of mass $$10$$ $$kg.$$ is hinged at the left end is suspended with the help of spring and damper arrangement as shown in the figure where $$K = 2kN/m,$$ $$C =500Ns/m$$ and the stiffness of the torsional spring $${K_\theta }$$ is 1 kN/m/rad. Ignore the hinge dimensions.

The un-damped natural frequency of oscillations of the bar about the hinge point is

A uniform rigid slender bar of mass $$10$$ $$kg.$$ is hinged at the left end is suspended with the help of spring and damper arrangement as shown in the figure where $$K = 2kN/m,$$ $$C =500Ns/m$$ and the stiffness of the torsional spring $${K_\theta }$$ is 1 kN/m/rad. Ignore the hinge dimensions.

The damping coefficient in the vibration equation is given by