Suppose a simple harmonic oscillator solution for a mass$-$spring system is given by x$($t$)=0\mathrm{.}7$ cos$(8$t $+1\mathrm{.}9),$ where all MKS units are assumed.

$$

For this solution,

$($a$)$ the amplitude is $[$ Select $]["5\mathrm{.}6","\mathrm{.}49","8","0\mathrm{.}7","4\mathrm{.}21"]$ m;

$($b$)$ the angular frequency is $[$ Select $]["0\mathrm{.}7","8","1\mathrm{.}27","1\mathrm{.}9"]$ rad$/$s;

$($c$)$ the phase shift is $[$ Select $]["8","1\mathrm{.}9","0\mathrm{.}7"]$ rad;

$($d$)$ the frequency is $[$ Select $]["1\mathrm{.}58","1\mathrm{.}9","8","0\mathrm{.}785","1\mathrm{.}27"]$ Hz;

$($e$)$ the period is $[$ Select $]["0\mathrm{.}672","1\mathrm{.}86","1\mathrm{.}27","0\mathrm{.}785"]$ s;

$($f$)$ the maximum speed is $[$ Select $]["5\mathrm{.}6","3\mathrm{.}6","4\mathrm{.}2","2\mathrm{.}8"]$ m$/$s;

$($g$)$ the maximum acceleration is $[$ Select $]["18\mathrm{.}6","22\mathrm{.}4","32\mathrm{.}5","44\mathrm{.}8"]$ m$/$s$2$;

$($h$)$ the position at t $=0$ s is $[$ Select $]["0\mathrm{.}6996","-0\mathrm{.}334","-0\mathrm{.}226","-0\mathrm{.}523"]$ m;

$($i$)$ the velocity at t $=0$ s is $[$ Select $]["-2\mathrm{.}62","-4\mathrm{.}15","-5\mathrm{.}30","2\mathrm{.}62","5\mathrm{.}30"]$ m$/$s;

$($j$)$ the acceleration at t $=0$ s is $[$ Select $]["-13\mathrm{.}2","14\mathrm{.}48","8\mathrm{.}92","-5\mathrm{.}80","19\mathrm{.}3"]$ m$/$s$2$;

$($k$)$ Find the first time t $>0$ that the mass reaches x $=0.[$ Select $]["0\mathrm{.}155","0\mathrm{.}785","0\mathrm{.}352","0\mathrm{.}265","0\mathrm{.}418"]$

$($l$)$ Find the first time t $>0$ that the speed is $0.[$ Select $]["0\mathrm{.}261","0\mathrm{.}352","0\mathrm{.}405","0\mathrm{.}155"]$