Extra Credit Problem: Simple Harmonic Motion with a Horizontal Spring

A $0\mathrm{.}80$ kg mass is attached to a horizontal spring with spring constant $k=24\frac{N}{m}$ on a frictionless surface. The mass is pulled to a maximum displacement $A=0\mathrm{.}40m$ from equilibrium and released.

$1.$Calculate the total mechanical energy of the system.

$2.$Determine the period and frequency of the motion.

$3.$Determine the amplitude, maximum velocity, and maximum acceleration.

$4.$Find the velocity and acceleration of the mass when it is $\frac{1}{4}$ of the way to the equilibrium position.

$($Please make sure to describe the step by step process if you can$)$