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

A frictionless piston-cylinder device contains a gas initially at $$0.8MPa$$ and $$0.015$$ $${m^3}.$$ It expands quasi-statically at constant temperature to a final volume of $$0.030$$ $${m^3}.$$ The work output (in $$kJ$$) during this process will be