A vibratory system consists of mass $m$, a vertical spring of stiffness $2k$ and a horizontal spring of stiffness $k$. The end $A$ of the horizontal spring is given a horizontal motion $x_A = a \sin \omega t$. The other end of the spring is connected to an inextensible rope that passes over two massless pulleys as shown.

Assume $m = 10 kg$, $k = 1.5$ kN/m, and neglect friction.

The magnitude of critical driving frequency for which the oscillations of mass $m$ tend to become excessively large is _____ rad/s (answer in integer).

A furnace can supply heat steadily at 1200 K at a rate of 24000 kJ/min. The maximum amount of power (in kW) that can be produced by using the heat supplied by this furnace in an environment at 300 K is

Which one of the following statements regarding a Rankine cycle is FALSE?

A piston-cylinder arrangement shown in the figure has a stop located 2 m above the base. The cylinder initially contains air at 140 kPa and 350 °C and the piston is resting in equilibrium at a position which is 1 m above the stops. The system is now cooled to the ambient temperature of 25 °C. Consider air to be an ideal gas with a value of gas constant $R = 0.287$ kJ/(kg·K).

The absolute value of specific work done during the process is ________ kJ/kg (rounded off to 1 decimal place)