Use the worked example above to help you solve this problem.

$($a$)$ Find the amplitude, frequency, and period of motion for an object vibrating at the end of a horizontal spring if the equation for its position as a function of time is the following.

x $=(0\mathrm{.}270$ m$)$ cos

$8\mathrm{.}00$

$$t

A $=$ mf $=$ HzT $=$ s

$($b$)$ Find the maximum magnitude of the velocity and acceleration.

vmax $=$ m$/$samax $=$ m$/$s$2$

$($c$)$ What are the position, velocity, and acceleration of the object after $1\mathrm{.}40$ s has elapsed?