A single-cylinder engine has a total mass of \(150 \mathrm{~kg}\). Its reciprocating mass is \(5 \mathrm{~kg}\), and the rotating mass is \(2.5 \mathrm{~kg}\). The stroke ( \(2 \mathrm{r})\) is \(15 \mathrm{~cm}\), and the speed is \(600 \mathrm{rpm}\).

(a) If the engine is mounted floating on very weak springs, what is the amplitude of vertical vibration of the engine?

(b) If the engine is mounted solidly on a rigid foundation, what is the alternating force amplitude transmitted? Assume the connecting rod to be of infinite length.