A small mass that is oscillating with simple harmonic motion on a vertical spring has a maximum amplitude of $0\mathrm{.}25$ m and maximum speed $4\mathrm{.}8$ m$/$s$.$ When a different mass $(0\mathrm{.}750$ kg$)$ simply hangs at rest from the spring, it stretches the spring $0\mathrm{.}15$ m$.$ Find $($a$)$ the angular frequency $$ of the first mass, $($b$)$ the frequency of the first mass, $($c$)$ the period of the first mass, $($d$)$ the maximum acceleration of the first mass, $($e$)$ the total energy of the system with the first mass, $($f$)$ the amplitude of motion of the first mass, $($g$)$ the maximum velocity of the first mass, $($h$)$ the maximum acceleration of the first mass, $($i$)$ the displacement of the first mass from the equilibrium position at t $=1\mathrm{.}5$ s$,($j$)$ the velocity of the first mass at t $=1\mathrm{.}5$ s$,($k$)$ the acceleration of the first mass at t $=1\mathrm{.}5$ s$,$ and $($l$)$ the spring constant of the spring.