Problem $2.(25$ Points$)$

The response of a system is given by

$x(t)=0\mathrm{.}003cos(30t)+0\mathrm{.}004sin(30t)$

Determine:

$($a$)$ The amplitude of motion,

$($b$)$ The period of motion,

$($c$)$ The frequency in Hz $,$

$($d$)$ the frequency in rad$/$s$,$

$($e$)$ the frequency in rpm$,$

$($f$)$ The phase angle; consider the compact response has the form

$x(t)=xsin(t+)$

$($g$)$

$($h$)$ The phase lag

$($i$)$ The compact response of system