Problem
Question 13 A simple pendulum has a length of $0.532 \mathrm{~m}$. The pendulum bob of mass $40.0 \times 10^{-3} \mathrm{~kg}$ is displaced $2.50 \times 10^{-2} \mathrm{~m}$ from equilibrium and released. It then moves with simple harmonic motion (S.H.M.). a) i. Determine the time period of the pendulum. [ 2 ] ii. Determine the maximum acceleration of the pendulum bob. [ 2 ] iii. Sketch a graph to show how the acceleration varies with [ 3 ] displacement for the pendulum. The graph should show both axes with labels and unit, appropriate values indicated on each axis and a line of best fit. iv. Determine the total kinetic and potential energy of the pendulum [3] bob.
Solution
Step 1 ：Given that the length of the pendulum, L = 0.532 m, and the acceleration due to gravity, g = 9.81 m/s^2.
Step 2 ：Use the formula for the period of a simple pendulum, which is given by \(T = 2\pi\sqrt{\frac{L}{g}}\).
Step 3 ：Substitute the given values into the formula to calculate the period.
Step 4 ：\(T = 2\pi\sqrt{\frac{0.532}{9.81}}\)
Step 5 ：Calculate the value to get \(T = 1.4631915379086071\)
Step 6 ：Round the final answer to two decimal places to get \(\boxed{1.46 \, \text{s}}\).
