Pendulum
Laboratory Report : Experiment One
Title: Determination of the acceleration due to gravity with a simple pendulum
Introduction and Theory: A simple pendulum performs simple harmonic motion, i.e. its periodic motion is defined by an acceleration that is proportional to its displacement and directed towards the centre of motion. It can be shown that the period T of the swinging pendulum is proportional to the square root of the length l of the pendulum: T2= (4π2l)/g
with T the period in seconds, l the length in meters and g the gravitational acceleration in m/s2. Our raw data should give us a square-root relationship between the period and the length. Furthermore, to find an accurate value for ‘g’, we will also graph T2 versus the length of the pendulum. This way, we will be able to obtain a straight-line graph, with a gradient equal to 4π2g–1.
Procedure: Refer to lab manual.
Measurement / Data:
Length of Pendulum ( l +/- 0.1 cm) | Time for 20 Oscillations (s) | Time for 1 Oscillation (Periodic Time) T (s) | T^2 ( s^2) | | 1 | 2 | Mean | | | 35 | 24.00 | 23.87 | 23.94 | 1.20 | 1.43 | 45 | 26.50 | 26.75 | 26.63 | 1.33 | 1.77 | 55 | 29.94 | 29.81 | 29.88 | 1.49 | 2.23 | 65 | 32.44 | 32.31 | 32.38 | 1.62 | 2.62 | 75 | 35.06 | 35.00 | 35.03 | 1.75 | 3.07 | 85 | 37.06 | 36.87 | 36.97 | 1.85 | 3.42 | 95 | 39.25 | 39.19 | 39.22 | 1.96 | 3.85 |
Length of Pendulum ( l +/- 0.1 cm) | Time for 20 Oscillations (s) | Time for 1 Oscillation (Periodic Time) T (s) | T^2 ( s^2) | | 1 | 2 | Mean | | | 35 | 24.87 | 25.19 | 25.03 | 1.25 | 1.57 | 65 | 33.94 | 33.44 | 33.69 | 1.68 | 2.84 | 95 | 40.25 | 40.31 | 40.28 | 2.01 | 4.06 |
Length of Pendulum ( l +/- 0.1 cm) | Time for 20 Oscillations (s) | Time for 1 Oscillation (Periodic Time) T (s) | T^2 ( s^2) | | 1 | 2 | Mean | | | 35 | 23.56 | 23.62 | 23.59 | 1.20 | 1.39 | 65 | 32.75 | 32.00 | 32.38 | 1.62 | 2.62 | 95 | 38.11 | 38.87 | 38.49 | 1.92 | 3.70 |
Title: Determination of the acceleration due to gravity with a simple pendulum
Introduction and Theory: A simple pendulum performs simple harmonic motion, i.e. its periodic motion is defined by an acceleration that is proportional to its displacement and directed towards the centre of motion. It can be shown that the period T of the swinging pendulum is proportional to the square root of the length l of the pendulum: T2= (4π2l)/g
with T the period in seconds, l the length in meters and g the gravitational acceleration in m/s2. Our raw data should give us a square-root relationship between the period and the length. Furthermore, to find an accurate value for ‘g’, we will also graph T2 versus the length of the pendulum. This way, we will be able to obtain a straight-line graph, with a gradient equal to 4π2g–1.
Procedure: Refer to lab manual.
Measurement / Data:
Length of Pendulum ( l +/- 0.1 cm) | Time for 20 Oscillations (s) | Time for 1 Oscillation (Periodic Time) T (s) | T^2 ( s^2) | | 1 | 2 | Mean | | | 35 | 24.00 | 23.87 | 23.94 | 1.20 | 1.43 | 45 | 26.50 | 26.75 | 26.63 | 1.33 | 1.77 | 55 | 29.94 | 29.81 | 29.88 | 1.49 | 2.23 | 65 | 32.44 | 32.31 | 32.38 | 1.62 | 2.62 | 75 | 35.06 | 35.00 | 35.03 | 1.75 | 3.07 | 85 | 37.06 | 36.87 | 36.97 | 1.85 | 3.42 | 95 | 39.25 | 39.19 | 39.22 | 1.96 | 3.85 |
Length of Pendulum ( l +/- 0.1 cm) | Time for 20 Oscillations (s) | Time for 1 Oscillation (Periodic Time) T (s) | T^2 ( s^2) | | 1 | 2 | Mean | | | 35 | 24.87 | 25.19 | 25.03 | 1.25 | 1.57 | 65 | 33.94 | 33.44 | 33.69 | 1.68 | 2.84 | 95 | 40.25 | 40.31 | 40.28 | 2.01 | 4.06 |
Length of Pendulum ( l +/- 0.1 cm) | Time for 20 Oscillations (s) | Time for 1 Oscillation (Periodic Time) T (s) | T^2 ( s^2) | | 1 | 2 | Mean | | | 35 | 23.56 | 23.62 | 23.59 | 1.20 | 1.39 | 65 | 32.75 | 32.00 | 32.38 | 1.62 | 2.62 | 95 | 38.11 | 38.87 | 38.49 | 1.92 | 3.70 |