Determine amplitude and period of an added cosine

Question

Graph

$g(t)=2\cos(\frac{\pi}{3}t)$ (dashed curve)

$f(t)=g(t) + Acos(\omega t)$ (drawn-through curve)

Obviously $A = 1$. But what is the value of $\omega$?

Answer 1

Over the interval $(0,6)$, your perturbed function $f$ oscillates three times around the base function $g$. That means that the perturbation must have three times the frequency of $g$ that is it must have $\omega=\pi$.