The graph from a pendulum with the greatest amplitude displays the waveform with the highest peaks and deepest troughs from the equilibrium position. Amplitude represents the pendulum's maximum displacement from the center, affecting the peak and trough heights on the graph.
The graph created by a pendulum with the greatest amplitude would be the one where the transverse waveform has the largest distance above and below the equilibrium position on the y-axis. In simple harmonic motion, such as that of a pendulum or a spring, the amplitude represents the maximum displacement from the equilibrium position.
If we have a graph with displacement on the y-axis and time on the x-axis, the amplitude is depicted as the height of the peaks (when the pendulum is farthest from the center) and the depth of the troughs (when the pendulum is equally far in the opposite direction), assuming no damping is present.
The correct answer to how an increase in amplitude and period affects the graph is: 'Larger amplitude would result in taller peaks and troughs and a longer period would result in greater separation in time between peaks.' This means that with a larger amplitude, the pendulum swings further from the equilibrium and thus the peaks and troughs of the graph would be more pronounced.
A longer period, on the other hand, indicates that it takes more time for the pendulum to complete one full swing, thus stretching the waveform out along the time axis, increasing the separation between successive peaks and troughs.