A $1\mathrm{.}50$ kg mass on a spring has displacement as a function of time given by x$($t$)=(7\mathrm{.}40$cm$)$ cos$[(4\mathrm{.}16$rad$/$s$)$r $-2\mathrm{.}42)$ Find $($a$)$ the time for one complete vibration; $($b$)$ the force constant of the spring; $($c$)$ the maximum speed of the mass; $($d$)$ the maximum force on the mass; $($ e$)$ the position, speed, and acceleration of the mass at t $=1\mathrm{.}00$ s; $($f$)$ the force on the mass at $1$hat time $.$