A compound gear train with gears P, Q, R and S has number of teeth 20, 40, 15 and 20, respectively. Gears Q and R are mounted on the same shaft as shown in the figure below. The diameter of the gear Q is twice that of the gear R. If the module of the gear R is 2 mm, the center distance in mm between gears P and S is

A flywheel connected to a punching machine has to supply energy of $$400$$ Nm while running at a mean angular speed of $$20$$ rad/s. If the total fluctuation of speed is not to exceed $$ \pm 20\% $$, the mass moment of inertia of the flywheel in kg-m² 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

A single degree of freedom system having mass $$1$$ $$kg$$ and stiffness $$10$$ $$kN/m$$ initially at rest is subjected to an impulse force of magnitude $$5$$ $$kN$$ for $${10^{ - 4}}$$ seconds. The amplitude in $$mm$$ of the resulting free vibration is