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Length of string, l/cm

Time taken

20 complete

oscillations /s

Period, T= t/20 /s

t1

t2

Mean, t

20.0

17.6

17.5

17.6

0.88

25.0

19.3

19.5

18.4

0.92

30.0

22.1

22.2

22.2

1.11

35.5

24.0

24.2

24.1

1.21

40.0

25.0

25.0

25.0

1.25

45.0

26.9

26.7

26.8

1.34

50.0

28.0

27.9

28.0

1.40

55.0

29.1

29.3

29.2

1.46

60.0

30.8

30.8

30.8

1.54

65.0

32.4

32.2

32.3

1.62

70.0

33.1

33.2

33.2

1.66

T

he pendulum is a body suspended from a fixed point so as to swing freely back and forth under the action of gravity. Its regular motion has served as the basis for measurement, as recognized by Galileo. Huygens applied the principle to clock mechanisms. Other applications include seismic instrumentation and the use by NASA to measure the physical properties of space flight payloads. The underlying equation is at the heart of many problems in structural dynamics. Structural dynamics deals with the prediction of a structure’s vibratory motions. Examples include the smoothness or bounciness of the car you ride in, the wing motion that you can see if you look out of the window of an airplane in a bumpy flight, the breaking up of roads and buildings in an earthquake, and anything else that crashes, bounces or vibrates. With this pendulum motion as a point of departure, complex structures can be analyzed.

T

he pendulum serves as an illustration of Newton’s Second Law, which states that for every force there is an equal and opposite reaction. The simpler experiments illustrate another of Newton’s laws, namely, that a body in motion continues in motion unless acted upon by another force. The pendulum offers an extensive array of experiments that can be done using easy to obtain, inexpensive materials. The measurements require no special skills and equipment. The graphical results of each experiment are given, and can be compared to the results calculated from a simple equation if desired.

1. Attach weight to the shortest string, then attach the other end of the string to a support, such as shown in Figure 1. Measure the length.

Figure 1

2. Lift the bob (keeping the string taut) so that the string angle from vertical is about 15 degrees. 3. Let go of the bob without pushing it. 4. note the time when it released, and count the bob’s return for 20 cycles. 5. note the time when the 20th cycle is completed. The period is this time divided by 20. 6. repeat the measurement several times and take the average result. 7. Then, repeat the experiment for several lengths ranging from 20.0 cm - 70.0 cm. 8. the readings are recorded in a suitable table.

Length of string, l/cm

Time taken

20 complete

oscillations /s

Period, T= t/20 /s

t1

t2

Mean, t

20.0

17.6

17.5

17.6

0.88

25.0

19.3

19.5

18.4

0.92

30.0

22.1

22.2

22.2

1.11

35.5

24.0

24.2

24.1

1.21

40.0

25.0

25.0

25.0

1.25

45.0

26.9

26.7

26.8

1.34

50.0

28.0

27.9

28.0

1.40

55.0

29.1

29.3

29.2

1.46

60.0

30.8

30.8

30.8

1.54

65.0

32.4

32.2

32.3

1.62

70.0

33.1

33.2

33.2

1.66

T/s

Graph of period, T/s against length, l/cm 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

1.11

1.21 1.25

1.46 1.4 1.34

1.54

1.62 1.66

0.88 0.92

1

2

3

4

5

6 l/cm

7

8

9 10 11

Based on the graph obtained, it is clearly proven that :

T

he longer the length of the string, the longer the time taken to complete an oscillations. or

T

he shorter the length of the string, the shorter the time taken to complete an oscillations. This conclusions can be made when the mass of the pendulum is kept constant. By mean that the same mass of pendulum is use in each experiment although the length of string are varies.