You have a two$-$wheel trailer that you pull behind your ATV. Two children with a combined mass of $86\mathrm{.}2$ kg hop on board for a ride through the woods and the springs $($one for each wheel$)$ each compress by $5\mathrm{.}37$ cm$.$ When you pull the trailer over a tree root in the trail, it oscillates with a period of $1\mathrm{.}24$ s$.$ Determine the following.

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

How is the force constant of a spring related to the force the spring exerts when it is stretched or compressed? N$/$m

$($b$)$ mass of the trailer

kg

$($c$)$ frequency of the oscillation

Hz

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