You have a two$-$wheel trailer that you pull behind your ATV. Two children with a combined mass of $62\mathrm{.}2$ kg hop on board for a ride through the woods and the springs $($one for each wheel$)$ each compress by $5\mathrm{.}97$ cm $.$ When you pull the trailer over a tree root in the trail, it oscillates with a period of $1\mathrm{.}34$ s $.$ Determine the following.

$($a$)$ force constant of the springs

$\backslash (5103\backslash$sim $\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash )$

$($b$)$ mass of the trailer

How is the period of oscillation for an oscillating mass related to the force constant of the spring and the mass suspended by the spring? kg

$($c$)$ frequency of the oscillation

$-$ Hz

$($d$)$ time it takes for the trailer to bounce up and down $10$ times $\backslash (\backslash$approx s $\backslash )$