1. **State the problem:** We want to find the sinusoidal wave function in the form $$V(t) = V_{\text{offset}} + V_0 \sin(\omega t)$$ given the measurements: - Minimum value $V_{\text{low}} = 2$ - Maximum value $V_{\text{top}} = 26$ - Peak-to-peak time $T_{\text{p2p}} = 72$ 2. **Find the vertical offset $V_{\text{offset}}$: ** The vertical offset is the midpoint between the maximum and minimum values: $$V_{\text{offset}} = \frac{V_{\text{top}} + V_{\text{low}}}{2} = \frac{26 + 2}{2} = 14$$ 3. **Find the amplitude $V_0$: ** The amplitude is half the difference between maximum and minimum: $$V_0 = \frac{V_{\text{top}} - V_{\text{low}}}{2} = \frac{26 - 2}{2} = 12$$ 4. **Find the angular frequency $\omega$: ** The period $T$ is given as $T_{\text{p2p}} = 72$, so $$\omega = \frac{2\pi}{T} = \frac{2\pi}{72} = \frac{\pi}{36}$$ 5. **Write the sinusoidal function: ** $$V(t) = 14 + 12 \sin\left(\frac{\pi}{36} t\right)$$ This function has amplitude 12, offset 14, and period 72, matching the original waveform. **Final answer:** $$V(t) = 14 + 12 \sin\left(\frac{\pi}{36} t\right)$$