Simple Pendulum Experiment: Measuring Gravity Acceleration

Experimental Procedure

Period Depending on the Mass of Oscillation

Two different masses were chosen for the experiment: one metal and one wood. Measurements were taken twice for 10 swings per mass, keeping the swing angle and the length of the pendulum equal. The procedure was repeated with the second mass. We determined the average time for each mass and calculated the period (T) using the equation: T = time / number of swings.

• The corresponding absolute error for each body was calculated through the formula: ΔT = Δt / n.
• The oscillation angle used was α = (10 ± 1)°.
• The pendulum length used was L = (31.5 ± 0.1) cm.
• An m vs. T plot was constructed.
• The experimental data are recorded in Table 1.

Period Depending on the Angle of Oscillation

• Three small angles were utilized: 5°, 10°, and 15°.
• Two measurements were taken for 10 swings at each angle, keeping the mass of the sphere and the length of the pendulum equal.
• The procedure was repeated for the other two angles.
• The average time for each angle was determined.
• The period for each was calculated using the equation mentioned above.
• The corresponding absolute error for each angle was determined.
• A mass of m = (7.3600 ± 0.0001) grams was used.
• The string length used was L = (31.5 ± 0.1) cm.
• An α vs. T graph was constructed.
• The data obtained are recorded in Table 2.

Period Depending on the Length of the Pendulum

• Seven different chord lengths were chosen for this phase.
• Two measurements were taken for 10 swings at a fixed rope length, keeping the swing angle and the mass of the sphere equal.
• The procedure was repeated for the other six chord lengths.
• The average time for each length was determined.
• The period of each was determined with the aforementioned equation.
• The period was squared (T²) and its absolute error was calculated.
• A mass of m = (7.3600 ± 0.0001) grams was used.
• An oscillation angle of α = (10 ± 1)° was used.
• The value of T² (T * T) and its absolute error were obtained.
• Graphs for T vs. L and T² vs. L were constructed.
• The data obtained are recorded in Table 3.

Data Analysis and Gravity Determination

From the graph of T² vs. L, the slope and cutoff of the line were obtained. These were compared with values obtained through the method of least squares (which requires the values of T² and L). The absolute errors of T² and L were also calculated using the least squares method.

The acceleration of gravity was determined from the equation relating the period of oscillation of a simple pendulum to its length: T² = (4π² · L) / g.

Since the equation of a line is represented by y = mx + b, we can see the relationship if we set Y = T² and X = L. From this, the slope of the line (m) is equal to the constant 4π² / g, and the constant term (b) is zero. Finally, the acceleration of gravity is calculated from the slope using the following equation: g = 4π² / m.