1. The problem involves analyzing two sinusoidal waves $x_1$ and $x_2$ with amplitudes 6 cm and 2 cm respectively, both plotted against time $t$ in seconds. 2. Both waves have the same period, and start at zero displacement at $t=0$. 3. Since the waves are sinusoidal and start at zero, we can model them as: $$x_1(t) = 6 \sin(\omega t)$$ $$x_2(t) = 2 \sin(\omega t)$$ where $\omega$ is the angular frequency. 4. The period $T$ can be observed from the graph as the time it takes for the wave to complete one full cycle. Given the peaks at $t=0.25$ s and $t=0.5$ s, the period is $T=0.5$ s. 5. Angular frequency $\omega$ is related to the period by: $$\omega = \frac{2\pi}{T} = \frac{2\pi}{0.5} = 4\pi \text{ rad/s}$$ 6. Therefore, the wave functions are: $$x_1(t) = 6 \sin(4\pi t)$$ $$x_2(t) = 2 \sin(4\pi t)$$ 7. These equations describe the displacement in cm of each wave at any time $t$ in seconds. Final answer: $$x_1(t) = 6 \sin(4\pi t), \quad x_2(t) = 2 \sin(4\pi t)$$