(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

Transcribed Image Text:

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