A mass $$m$$ attached to a spring is subjected to a harmonic force as shown in the figure. The amplitude of the forced motion is observed to be $$50$$ mm. The value of m (in kg) is

The natural frequency of a spring-mass system on earth is $${\omega _n}.$$ The natural frequency of this system on the moon (g_moon = g_earth/6) is

One kilogram of water at room temperature is brought into contact with a high temperature thermal reservoir. The entropy change of the universe is

In a steam power plant operating on the Rankine cycle, steam enters the turbine at $$4$$ $$MPa,$$ $${350^ \circ }C$$ and exits at a pressure of $$15$$ $$kPa.$$ Then it enters the condenser and exits as saturated water. Next, a pump feeds back the water to the boiler. The adiabatic efficiency of the turbine is $$90\% $$. The thermodynamic states of water and steam are given in the table.

$$h$$ is specific enthalpy, $$s$$ is specific entropy and $$v$$ the specific volume; subscripts $$f$$ and $$g$$ denote saturated liquid state and saturated vapour state.

The net work output $$(kJ/kg)$$ of the cycle is