Compare the R² values for the graph of period vs. length and the graph of period vs. the square root of the length and explain whether your results support the equation for the period of a pendulum.

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Author:Raymond A. Serway, John W. Jewett
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Chapter15: Oscillatory Motion
Section: Chapter Questions
Problem 15.42P: A very light rigid rod of length 0.500 m extends straight out from one end of a meterstick. The...
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Compare the R² values for the graph of period vs. length and the graph of period vs. the square root of the length and explain whether your results support the equation for the period of a pendulum. 

Experiment 1 (changing angle) Length of Pendulum (m) Angle of Release # Of Oscillations
Time 1
Time 2
Time 3
Avg Time (s)
Avg Period (s) Expected Period Percent Error
Standard Deviation
1
0.22
40
10
10.8
10.73
10.37
10.63
1.063
0.941
13.000
0.086
2
0.22
50
10
10.98
11.16
11.09
11.08
1.108
0.941
17.800
0.118
3
0.22
60
10
11.4
11.5
11.4
11.4
1.14
0.941
21.200
0.141
4
0.22
70
10
11.52
11.54
11.72
11.59
1.159
0.941
23.200
0.154
Experiment 2 (changing length)
5
0.22
40
10
10.8
10.73
10.37
10.63
1.063
0.941
13.000
0.086
6
0.29
40
10
12.1
12.05
12.06
12.07
1.207
1.080
11.700
0.090
7
0.36
40
10
13.25
13.33
13.09
13.22
1.322
1.204
9.800
0.084
8
0.43
40
10
14.39
14.45
14.4
14.41
1.441
1.315
9.500
0.089
Transcribed Image Text:Experiment 1 (changing angle) Length of Pendulum (m) Angle of Release # Of Oscillations Time 1 Time 2 Time 3 Avg Time (s) Avg Period (s) Expected Period Percent Error Standard Deviation 1 0.22 40 10 10.8 10.73 10.37 10.63 1.063 0.941 13.000 0.086 2 0.22 50 10 10.98 11.16 11.09 11.08 1.108 0.941 17.800 0.118 3 0.22 60 10 11.4 11.5 11.4 11.4 1.14 0.941 21.200 0.141 4 0.22 70 10 11.52 11.54 11.72 11.59 1.159 0.941 23.200 0.154 Experiment 2 (changing length) 5 0.22 40 10 10.8 10.73 10.37 10.63 1.063 0.941 13.000 0.086 6 0.29 40 10 12.1 12.05 12.06 12.07 1.207 1.080 11.700 0.090 7 0.36 40 10 13.25 13.33 13.09 13.22 1.322 1.204 9.800 0.084 8 0.43 40 10 14.39 14.45 14.4 14.41 1.441 1.315 9.500 0.089
The Effect of Different Lengths on the Period of a Pendulum
The Effect of Different Angles on the Period of a Pendulum
Avg Period (s) vs. Square root of Length
17.8*x + 6.78 R = 0.997
- 3.2E-03"x + 0.942 R = 0.968
2.01*x + 0.121 R = 0.999
15
1.25
1.5
1.00
10
1.0
0.75
0.50
0.5
0.25
0.0
0.25
0.00
40
0.30
0.35
0.40
50
60
70
0.50
0.55
0.60
0.65
Length (m)
Angle (degrees)
Square root of Length (m)
Average Period (s)
Average Period (s)
(s) pouad BAy
Transcribed Image Text:The Effect of Different Lengths on the Period of a Pendulum The Effect of Different Angles on the Period of a Pendulum Avg Period (s) vs. Square root of Length 17.8*x + 6.78 R = 0.997 - 3.2E-03"x + 0.942 R = 0.968 2.01*x + 0.121 R = 0.999 15 1.25 1.5 1.00 10 1.0 0.75 0.50 0.5 0.25 0.0 0.25 0.00 40 0.30 0.35 0.40 50 60 70 0.50 0.55 0.60 0.65 Length (m) Angle (degrees) Square root of Length (m) Average Period (s) Average Period (s) (s) pouad BAy
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