In the figure shown, the spring deflects by $$\delta $$ to position A ( the equilibrium position) when a mass $$m$$ is kept on it. During free vibration, the mass is at position $$B$$ at some instant. The change in potential energy of the spring mass system from position $$A$$ to position $$B$$ is

The assembly shown in the figure is composed of two massless rods of length $$l$$ with two particles, each of mass $$m$$. The natural frequency of this assembly for small oscillations is

A spring mass $$-$$ dashpot system is shown in the figure. The spring stiffness is $$K,$$ mas is $$m$$, and the viscous damping coefficient is $$c$$. The system is subjected to a force $$\,{F_0}\cos \omega t\,\,$$ as shown. Write the equations of motion which are needed to determine $$x.$$ (No need to determined $$x.$$)

A small steam whistle (perfectly insulated and doing no shaft work) causes a drop of $$0.8$$ $$kJ/kg$$ in the enthalpy of steam from entry to exit. If the kinetic energy of the steam at entry is negligible, the velocity of the steam at exit is