The following data refers to a cam with circular nose and flanks operating the suction valve of a four-stroke petrol engine:

Lift \(=10 \mathrm{~mm}\), Least radius of cam \(=20 \mathrm{~mm}\), Nose radius \(=2.5 \mathrm{~mm}\), Crank angle when suction valve opens after TDC \(=4^{\circ}\), Crank angle when suction valve closes after \(\mathrm{BDC}=50^{\circ}\), camshaft speed \(=1000 \mathrm{rpm}\).

The follower is of flat-faced type. Determine

(a) the maximum velocity of valve,

(b) the maximum acceleration and retardation of valve, and

(c) maximum force to be exerted by the spring to overcome inertia of the valve parts of weight \(0.2 \mathrm{~kg}\).