# Effect of changing length on period of a pendulum

Topics: Measurement, Pendulum, Harmonic oscillator Pages: 4 (1054 words) Published: May 6, 2014
﻿Aim
What is the effect of differing pendulum length on its period? Hypothesis
If the length of the pendulum is decreased, the period will decrease. Variables
Independent: The length of the pendulum (cm)
Dependent: The period of the pendulum (s)
Controlled:
The weight of the swinging mass
The angle for maximum displacement
Materials:
Pendulum (can be as simple as a mass tied to string attached to a piece of cardboard) Retort stand and clamp
Stopwatch
Ruler
Protractor
Masking tape
Method
1. Adjust the length of the pendulum to a desired starting point, using masking tape. 2. Use a retort stand and clamp to hang the pendulum perpendicular to the tabletop. 3. Record the time taken for 10 full cycles of the oscillation using a stopwatch. Ensure that the angle for maximum displacement of the pendulum is kept constant (this can be achieved by using a protractor). Repeat 2 times. 4. Divide the total time by ten to find the period of the pendulum and record. 5. Repeat steps 1-4 five times, decreasing the length of the pendulum by 10 cm incraments each test. Results table with uncertainties

Pendulum length (cm) +/- 0.1
Time taken for 10 cycles (s) +/- 0.01
Period of pendulum (s) +/-0.002
Average Period of pendulum (s) +/- 0.002
Angle of maximum displacement (°) +/- 1
71.5 a)
17.06
1.706
1.714
20
b)
17.21
1.721

20
61.5 a)
15.81
1.581
1.580
20
b)
15.79
1.579

20
51.5 a)
14.50
1.450
1.447
20
b)
14.44
1.444

20
41.5 a)
13.00
1.300
1.304
20
b)
13.07
1.307

20
31.5 a)
11.31
1.131
1.134
20
b)
11.37
1.137

20

Uncertainties:
Measurement of pendulum length, +/- 0.1 cm. This was measured with a ruler where the smallest unit shown was 0.1 cm. Half of this number (0.05 cm) is the uncertainty, but because there was uncertainty at either end of the measurement, this must be doubled. Therefore the uncertainty in length was 0.1 cm. Time measurement, +/-...

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