Question 13
A simple pendulum has a length of $0.532 m$ . The pendulum bob of mass $40.0 \times 10^{- 3} kg$ is displaced $2.50 \times 10^{- 2} m$ 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.

Answer

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Answer

Round the final answer to two decimal places to get $1.46 s$ .

Steps

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 $T = 2 π \sqrt{\frac{L}{g}}$ .

Step 3 ：Substitute the given values into the formula to calculate the period.

Step 4 ： $T = 2 π \sqrt{\frac{0.532}{9.81}}$

Step 5 ：Calculate the value to get $T = 1.4631915379086071$

Step 6 ：Round the final answer to two decimal places to get $1.46 s$ .