Given figure shows a piston driving a crank o p pivoted at

Question

Given Figure shows a piston driving a crank O P pivoted at the end O. The piston slides in a straight cylinder and the crank is made to rotate with constant angular velocity ω. Find the distance O Q in terms of the lengths b, c and the angle θ. Show that, when b/c is small, O Q is given approximately by

OQ = c + b cos θ - (b²/2c)(sin² θ ),

on neglecting (b/c)⁴ and higher powers. Using this approximation, find the maximum acceleration of the piston.