A point mass is executing simple harmonic motion with an amplitude of $$10$$ mm and frequency of $$4$$ Hz. The maximum acceleration (m/s²) of the mass is _________.

If two nodes are observed at a frequency of $$1800$$ rpm during whirling of a simply supported long slender rotating shaft, the first critical speed of the shaft in rpm is

The natural frequency of a spring-mass system on earth is $${\omega _n}.$$ The natural frequency of this system on the moon (g_moon = g_earth/6) is

The rotor shaft of a large electric motor supported between short bearings at both the ends shows a deflection of $$1.8$$ mm in the middle of the rotor. Assuming the rotor to be perfectly balanced and supported at knife edges at both the ends, the likely critical speed (in rpm) of the shaft is