The number of degrees of freedom of the planetary gear train shown in the figure is

In a spring-mass system the mass is m and the spring constant is $$k$$. The critical damping coefficient of the system is $$0.1$$ kg/s. In another spring mass system, the mass is $$2m$$ and the spring constant is $$8k$$. The critical damping coefficient (in kg/s) of this system is __________

A single-degree-freedom spring mass system is subjected to a sinusoidal force of $$10$$ N amplitude and frequency $$\omega $$ along the axis of the spring. The stiffness of the spring is $$150$$N/m, damping factor is $$0.2$$ and the undamped natural frequency is $$10$$$$\omega $$. At steady state, the amplitude of vibration (in m) is approximately

In a Rankine cycle, the enthalpies at turbine entry and outlet are $$3159$$ $$kJ/kg$$ and $$2187$$ $$kJ/kg$$ respectively. If the specific pump work is $$2$$ $$kJ/kg,$$ the specific steam consumption (in $$kg/k$$$$W$$-$$h$$) of the cycle based on net output is ________________