The graphs on the computer screen would look like this -
Time vs displacement for the in-phase oscilations
Time vs displacement for the out of -phase oscilations -
Time vs displacement for the beats
\(\omega_{1}\) and \(\omega_{2} \) can be deduced from the beat graph using this equation-
$$\theta(t) = \theta_{0}cos\left[\left(\frac{\omega_{1} - \omega_{2}}{2}\right)t
\right]cos\left[\left(\frac{\omega_{1} + \omega_{2}}{2}\right)t\right]$$
$$\omega_{b} = \frac{\omega_{1} - \omega_{2}}{2}$$
$$\omega_{f} = \frac{\omega_{1} + \omega_{2}}{2}$$