The rotor shaft of a large electric motor supported between short bearings at both the ends shows a deflection of $$1.8$$ mm in the middle of the rotor. Assuming the rotor to be perfectly balanced and supported at knife edges at both the ends, the likely critical speed (in rpm) of the shaft is

An automotive engine weighing $$240$$ kg is supported on four springs with linear characteristics. Each of the front two springs have a stiffness of $$16$$ MN/m while the stiffness of each rear spring is $$32$$ MN/m. The engine speed (in rpm), at which resonance is likely to occur, is

A vehicle suspension system consists of a spring and a damper. The stiffness of the spring is $$3.6$$ kN/m and the damping constant of the damper is $$400$$ Ns/m. If the mass is $$50$$ kg, then the damping factor ($$\xi $$) and damped natural frequency ($${f_n}$$) respectively are

A compressor undergoes a reversible, steady flow process. The gas at inlet and outlet of the compressor is designated as state $$1$$ and state $$2$$ respectively. Potential and kinetic energy changes are to be ignored. The following notations are used:
$$v=$$ specific volume and $$P=$$ pressure of the gas.
The specific work required to be supplied to the compressor for this gas compression process is