In a pendulum experiment, the period (T) of the pendulum is the time it takes for one complete back-and-forth swing. The period is primarily determined by the length of the pendulum and the acceleration due to gravity.
When the angular amplitude (the maximum angle from the vertical position) of a pendulum is varied, the relationship between the period and angular amplitude depends on the type of pendulum being used. There are two general cases to consider: small-angle approximation and large-angle oscillations.
Small-Angle Approximation: For small angular amplitudes (typically less than 15 degrees), the pendulum's motion can be approximated as simple harmonic motion. In this case, the graph of period (T) vs. angular amplitude is nearly linear. As the angular amplitude increases slightly, the period of the pendulum also increases slightly, but the relationship is relatively constant. The graph would appear as a straight line with a slight positive slope.
Large-Angle Oscillations: For larger angular amplitudes, the pendulum no longer follows simple harmonic motion, and the relationship between period and angular amplitude becomes more complex. The period of a pendulum for large angles is longer than that of small angles. As the angular amplitude increases further, the period of the pendulum increases significantly. The graph would show a nonlinear curve, likely resembling an elongated "S" shape, with the period increasing more rapidly as the angular amplitude increases.
It's worth noting that the precise shape of the graph may also be influenced by factors such as air resistance, mass distribution, and other experimental conditions. Therefore, experimental data should be collected to determine the specific relationship between period and angular amplitude for a given pendulum system.