A simple pendulum performs oscillations of period T in a vertical plane - AQA - A-Level Physics - Question 1 - 2020 - Paper 3

To determine the amplitude A_0, set up the pendulum as shown in Figure 2. Release the pendulum from a known height and observe the amplitude using a ruler or measuring tape. Measure the maximum displacement of the pendulum from the equilibrium position on both sides and average these values to find A_0.

From Figure 3, identify the values of period T corresponding to different amplitudes. Plot these points and draw a line of best fit. Calculate the percentage increase in T as follows:

ext{Percentage Increase} = rac{T_2 - T_1}{T_1} imes 100 where T_1 is the period at the initial amplitude A_0 and T_2 is the period at the increased amplitude.

Calculate the average of the six recorded values of A_n from Table 1. The average should be:

A_n = rac{0.217 + 0.240 + 0.225 + 0.223 + 0.218 + 0.224}{6} This gives the final recorded value of A_n.

To calculate the percentage uncertainty, take the range of values in Table 1:

ext{Uncertainty} = rac{0.240 - 0.217}{2} = 0.0115 Then, the percentage uncertainty is given by:

ext{Percentage Uncertainty} = rac{ ext{Uncertainty}}{A_n} imes 100

Using values provided in Table 2, calculate ln(A_n / m) for each n. Plot these values on Figure 4, ensuring proper scaling and labeling of axes. Each point should correspond to an n value with its respective ln(A_n / m).

From the graph of ln(A_n / m) against n, the intercept at n=0 will give the value of ln(A_0 / m). To find A_0, exponentiate the intercept:

$A_0 = e^{ ext{intercept}} imes m$ This will provide the initial amplitude of the pendulum.