The total sleeve movement in a Hartnell governor is 3 cm. The mass of the rotating balls is 1.5 kg each. At the mid-position of the sleeve, the sleeve arm, which is 6.5 cm long, is horizontal. The ball arm has a length of 7.5 cm. At the mid-position of the sleeve, the balls rotate at a radius of 10.5 cm.
Due to maladjustment of the spring, the equilibrium governor speed at the topmost position of the sleeve is 415 r.p.m. and that corresponding to the lowest position is 430 r.p.m.
Determine (i) the stiffness and initial compression of the spring and (ii) the required initial compression of the spring to give an equilibrium speed at the topmost position which is 10 r.p.m. more than that at the lowest position. Neglect the moment due to the weight of the balls.