A $0\mathrm{.}50-$kg box is attached to an ideal spring of force constant $($spring constant$)20$ N$/$m on a

horizontal, frictionless floor. The box oscillates in simple harmonic motion and has a speed of

$1\mathrm{.}5$ m$/$s at the equilibrium position.

$($a$)$ What is the amplitude of vibration?

$($b$)$ At what distance from the equilibrium position are the kinetic energy and the potential

energy the same?