Design a cam to raise a valve with simple harmonic motion through 50 mm in 1/3 of arevolution, keep if fully raised through 1/12 revolution and to lower it with harmonicmotion in 1/6 revolution. The valve remains closed during the rest of the revolution. Thediameter of the roller is 20 mm and the minimum radius of the cam is 25 mm. Thediameter of the camshaft is 25 mm. The axis of the valve rod passes through the axis ofthe camshaft. If the camshaft rotates at uniform speed of 100 r.p.m.; find the maximumvelocity and acceleration of a valve during raising and lowering.