A single-cylinder vertical diesel engine has a mass of \(350 \mathrm{~kg}\) and is mounted on a steel frame. The static deflection due to the weight of the frame is \(2 \mathrm{~mm}\). The reciprocating masses of the engine amounts to \(15 \mathrm{~kg}\) and the stroke of the engine is \(150 \mathrm{~mm}\). A dashpot with a damping coefficient of \(2 \mathrm{~N} / \mathrm{mm} / \mathrm{s}\) is also used to dampen the vibrations. In the steady state of the vibrations, determine

(a) amplitude of the vibrations if the driving shaft rotates at \(450 \mathrm{rpm}\), and

(b) the speed of the driving at resonance.