A vibratory system consists of a mass $$12.5$$ kg, a spring of stiffness $$1000$$ $$N/m,$$ and a dashpot with damping coefficient of $$15$$ $$Ns/m.$$

The value of logarithmic decrement is

Given below is an extract from steam tables.

Specific enthalpy of water in $$kJ/kg$$ at $$150$$ bar and $$ {45^ \circ }C$$ is

Assertion (A): Condenser is an essential equipment in a steam power plant.

Reason(R): For the same mass flow rate and the same pressure rise, a water pump requires substantially less power than a steam compressor.

Determine the correctness or otherwise of the following Assertion $$(a)$$ and the Reason$$(r).$$

Assertion(A): In a power plant working on a Rankine cycle, the regenerative feed water heating improves the efficiency of the steam turbine.

Reason(R): The regenerative feed water heating raises the average temperature of heat addition in the Rankine cycle.