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Q3. A cam operated valve moves vertically with simple harmonic motion. The camshaft speed is 600 rev/min and the valve is opened and closed during 160° of cam rotation. The valve travel is 100 mm and its mass is 1.8 kg. The valve opens downwards against a spring.

Calculate EACH of the following:

(a) the maximum velocity of the valve. (6)

(b) the instantaneous velocity of the valve when its displacement is 40 mm from the end of its downward travel. (2)

(c) the minimum spring force required at full opening to ensure that the valve remains in contact with the cam profile. (8)