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

x $=5\mathrm{.}00$ cos$$

$5$t $+$

$7$

where x is in centimeters and t is in seconds.

$($a$)$ At t $=0,$ find the position of the piston.

cm

$($b$)$ At t $=0,$ find velocity of the piston.

cm$/$s

$($c$)$ At t $=0,$ find acceleration of the piston.

cm$/$s$2$

$($d$)$ Find the period and amplitude of the motion.

period samplitude cm