Problem Set $$ Simple Harmonic Motion $1.$ In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression: $(5\mathrm{.}00$cm cos $2)6$ x t $=+$ 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. $($d$)$ Find the period and amplitude of the motion.