Chapter 12, Problem 14P

In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression

$x=5.00\cos \left(2t+\frac{\pi }{6}\right)$

where x is in centimeters and t is in seconds. At t = 0, find (a) the position of the piston, (b) its velocity, and (c) its acceleration. Find (d) the period and (e) the amplitude of the motion.