Here is the plot of the signal $x(t) = 4 \cos \left( 2\pi \frac{1}{3} t + \frac{\pi}{3} \right)$, showing its oscillation over time. You can observe the periodic nature of the signal, with a period of 3 seconds, as calculated earlier.

Would you like more details on any part of the solution, or do you have any questions?

Here are 5 related questions that expand on this concept:

1. How would the period of the signal change if the frequency were doubled?
2. What would the plot look like if the phase shift were $\frac{\pi}{2}$ instead of $\frac{\pi}{3}$?
3. How do you determine the amplitude of a cosine signal from its equation?
4. How does adding a sine component to the signal change its behavior?
5. What is the relationship between frequency and angular velocity in a cosine signal?

Tip: In periodic signals, the phase shift $\phi$ affects the horizontal translation but doesn't change the signal's frequency or amplitude.