A Pickering governor is driving a gramophone. Each disc attached to the centre of a leaf spring has a mass of 20 g. The width of each spring is 5 mm and thickness of 0.125 mm. The effective length of each spring is 40 mm. The distance from the spindle axis to the centre of gravity of the mass when the governor is at rest, is 10 mm. Find the speed of the governor in rpm when the sleeve has risen to a height of 0.8 mm. (E = 210kN/mm2)

I = bt3/12 =0.0008mm2 Length between fixed ends (L = 40-0.8 mm) Calculating delta from central deflection will give δ = 3.65 mm 3.65=0.51ω2 ω=2.675 rad/s.