(a) Show that for an object moving in simple harmonic motion, the speed of the object as a function of position is given by \(v(x)=\omega \sqrt{A^{2}-x^{2}}\).

(b) Noting that \(v_{x}=d x / d t\), isolate \(d t\) and integrate to determine how long it takes for an oscillator to move from its equilibrium position to some arbitrary position \(x)\).

Data from  Eq. 15.6

x(t) A sin o(t) === = A sin(wt) (simple harmonic motion),