$($a$)$ A simple harmonic oscillator's motion is given by

the graph at right. Describing its motion as a

function of time as x$($t$)=$Acos$(\backslash$omega t$+\backslash$phi $\_(0)),$ find

its amplitude, angular frequency, and phase

constant $\backslash$phi $\_(0).$

$**$ For finding $\backslash$phi $\_(0),$ don't just compare to a

calculator. Draw a unit circle or phasor diagram and figure out where the function

must be at t$=0$ to create this graph. Sho$($w$)/($e$)$xplain your work.

$($b$)$ What is the initial speed of the object, at t$=0?$ What is the maximum speed of the

object?

$($c$)$ If this graph represents the position of a $500$ g mass on a spring, what is the spring

constant? What is the total energy of the system?