Maximum fluctuation of kinetic energy in an engine has been calculated to be $$2600$$ J. Assuming that the engine runs at an average speed of $$200$$ rpm, the polar mass moment of inertia ( in kg.m² ) of a flywheel to keep the speed fluctuation within $$\, \pm 0.5\% $$ of the average speed is _______ .

Consider a flywheel whose mass $$M$$ is distributed almost equally between a heavy, ring-like rim of radius $$R$$ and a concentric disk-like feature of radius $$R/2$$. Other parts of the flywheel, such as spokes, etc, have negligible mass. The best approximation for $$\alpha ,$$ if the moment of inertia of the flywheel about its axis of rotation is expressed as $$\,\alpha M{R^2},\,\,$$ is ________.

What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plane is frictionless. The mass of the block is denoted by $$m$$ and the spring constants are denoted by $${k_1}$$ and $${k_2}$$ as shown below.

A pure substance at $$8$$ $$MPa$$ and $${400^ \circ }C$$ is having a specific internal energy of $$2864$$ $$kJ/kg$$ and a specific volume of $$0.03432\,{m^3}/kg.$$ Its specific enthalpy (in $$kJ/kg$$) is ____________