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

Match the following

Nitrogen gas (molecular weight $$28$$) is enclosed in a cylinder by a piston, at the initial condition of $$2$$ bar, $$298$$ $$K$$ and $$1\,\,{m^3}$$. In a particular process, the gas slowly expands under isothermal condition, until the volume becomes $$2{m^3}.$$ Heat exchange occurs with the atmosphere at $$298$$ $$K$$ during this process.

The work interaction for the Nitrogen gas is

A $$2$$ $$kW,$$ $$40$$ liter water heater is switched on for $$20$$ minutes. The heat capacity $${C_p}$$ for water is $$4.2$$ $$kJ/kg$$ $$K.$$ Assuming all the electrical energy has gone into heating the water, increase of the water temperature in degree centigrade is