A $200$ g load attached to a horizontal spring moves in simple harmonic motion with a period of $0\mathrm{.}430$ s$.$ The total mechanical energy of the spring$$load system is $4\mathrm{.}00$ J$.$

$($a$)$

What is the spring constant $($in N$/$m$)?$

N$/$m

$($b$)$

What is the amplitude $($in m$)$ of the motion?

m

$($c$)$

What If$?$ What is the percentage change in amplitude of motion if the total energy of the system is increased to $5\mathrm{.}00$ J$?$