Chapter 4.5, Problem 65E

Crankshaft A crank of radius r rotates with an angular frequency ω. It is connected to a piston by a connecting rod of length L (see figure). The acceleration of the piston varies with the position of the crank according to the function

$a(\theta )={\omega }^{2}r\left(\cos \theta +\frac{r\cos 2\theta }{L}\right).$

For fixed ω, L, and r, find the values of θ, with 0 ≤ θ ≤ 2π, for which the acceleration of the piston is a maximum and minimum.