$1.$ A small box with mass $0\mathrm{.}5$kg is attached to a spring $(200$ N$/$m$)$ and oscillates left and right with no dissipative forces. At time t $=0,$ the box is $25$cm to the right of its equilibrium position and moving left with a speed of $3$m$/$s$.($a$)$ What is the maximum distance to the right of its equilibrium position the box will reach? $($b$)$ What is the maximum speed the box will reach as it oscillates? $($c$)$ What is the period of the box$$s oscillations? $($d$)$ What is the maximum magnitude of acceleration the box will experience? $2.$ A box $(250$g$)$ attached to a spring begins at rest a distance of $30$cm from its equilibrium position. It oscillates with a period of $1\mathrm{.}25$s$.$ What is the maximum speed the box will reach as it oscillates? $3.$ One end of a small spring is attached to a wall, and a small mass is attached to the other end of the spring. The mass is pulled, stretching the spring $15$cm from the equilibrium position, and it is released from rest. As the mass oscillates on the spring, it reaches a maximum speed of $1\mathrm{.}85$m$/$s$.$ Assume there$$s no friction. $($a$)$ Starting the moment it is released, how long does it take for the mass to get to the point where the spring is compressed $15$cm$?($b$)$ If we took the same spring and the same mass but stretched the spring to $30$cm instead, how long would it take for the mass to get to the point where the spring is compressed $30$cm$?$