1.0 Title : The Simple Pendulum

2.0 Theoritical Fundamental

A small weight (or bob) suspended by a cord forms a simple pendulum. When the pendulum is swinging, the time of swing is found to be constant. This depends on the length of pendulum and is not affected by the weight of the bob or the arc of swing. The constant time of swing of a simple pendulum forms the basis of time counting in some clocks. It is known that the time of swing for a simple pendulum of length L is given by the formula

t=2π √L/g (1)

where, L=The Length of Pendulumt=Time

since π and g are constant, then

t = x√L (2)

This means that the time of swing of a simple pendulum is proportional to the root of its length. Objective of this experiment is to show that the time of a simple pendulum depends on its length. The same principle can as well be used to determine the value of the gravitational acceleration (g) as in equation 2.

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3.0 Apparatus

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4.0 Procedure

4.1 Preparation1. The mounting panel was secured in the vertical position.2. The adjustable hook is positioned3. The long screw was secured with nut while in place.4. A horizontal line was drawn on the mounting panel and marked as 0mm.5. Similar line at 130 mm, 160 mm,250 mm,280 mm and 360 mm are drawn below the

0 mm line.6. The cord on the plumb is adjusted by approximately 600 mm. The cord is tied with a

suitable knot so that it can be removed from the mounting panel when the experiment is completed.

3.2 Test 1

1. The rod slides so that the hook on is exactly on the 0 mm line.2. The plumb bob and the cord passed around the hook.3. The free end is clamped under the head of screw.4. The plumb bob has a dot stamped on its largest diameter which represents the centreof

gravity. This dot is positioned in line with the 160 mm mark ( Hence, the pendulum length, L is equal to 160 mm).

5. The pendulum swing with an amplitude of approximately 50 mm on either side of the static position (the hole-spacing on the mounting panel is used as a reference).

6. The time was recorded for 20 complete swings (a complete swing is counted when the plumb bob move from one extreme to another and return again).

7. The experiment was repeated to obtain an average result.8. Again, it was repeated for 100 mm amplitude.9. A 1N weight was added to the plum bob.10. For each 20 swings with amplitude of 50 mm and 100 mm, the time was recorded.

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3.3 Test 2

1. The 1N weight on the plumb bob is kept and lowered the cord until the bottom of the 1N weight is on the 250 mm mark.

2. The pendulum is set to swing with amplitude of approximately 100 mm and the time was recorded for 20 swings.

3. The bob is lowered until the length of pendulum is 360 mm and the time was recorded for 20 swings at 100 mm amplitude.

4. Again it is lowered at 490 mm and the time was recorded at the same amplitude for 20 swings.

5. Step 4 is repeated with the length at 640 mm.

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5.0 Result

Test 1

Amplitude (mm)

Length (mm)

T₁(s) T₂(s) T₃(s) Tavg=20 cycle (s)

Tavg = 1 cyle (s)

50 160 16.31 16.31 16.06 16.23 0.81100 160 16.59 16.91 16.78 16.76 0.84

Test 2

Weight (N) Amplitude Length T₁(s) T₂(s) T₃(s) Tavg (s)1 50 160 16.22 16.09 16.21 16.171 100 160 16.94 16.65 16.78 16.791 100 250 20.66 20.47 20.72 20.621 100 360 24.05 24.11 24.08 24.081 100 490 28.53 28.60 28.40 28.511 100 640 32.31 32.25 32.16 32.24

Amplitude (m)

Length of pendulum,L (m)

√L (m½) T=20 cycle (s) t = 1 cycle (s)

0.05 0.16 + 1N 0.40 16.17 0.810.10 0.16 + 1N 0.40 16.79 0.840.10 0.25 + 1N 0.50 20.62 1.030.10 0.36 + 1N 0.60 24.08 1.200.10 0.49 + 1N 0.70 28.51 1.430.10 0.64 + 1N 0.80 32.24 1.61

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Calculation

Since the pendulum length is same for both amplitude, the average time from both amplitude is taken for calculation :

Test 1

Plumb bob only,

L=0.16 m

√L ¿0.4m½

AverageTime=0.81+0.842

=0.83 s

Since,

√L = √ g2 πt

0.4=√ g2 π

¿)

g=9.17ms ²ˉ

Plumb Bob with 1N weight,

L = 0.16 m

√L = 0.4 m½

AverageTime=0.81+0.842

=0.83 s

Since,

√L = √ g2 πt

0.4=√ g2 π

¿)

g=9.17ms ²ˉ

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Test 2

Gradient of graph, m = y₂❑− y₁x2−x₁

= 0.7−01.43−0

= 0.49 m½ s ¹ˉ

√L = √ g2 πt ..........(1)

Y = mx ..........(2)

Compare (1) with (2),

m = √ g2 π

0.49 = √ g2 π

g = 9.48 ms ²ˉ

6.0 Discussion

1. Yes , the length of the pendulum will change its periodic time.The shorter the pendulum, the lesser time taken to complete a swing

2. Yes, the weight of the pendulum will also affect its periodic time. If more weight is added to the pendulum, it will take less time to complete a swing.

3. The longer the length of the pendulum, L, more time will be taken to complete a swing.Thus, the length affect the time directly.

4. Calculate the length of the pendulum and its weight, then adjust it so that a complete swing is equivalent to 1 second.Then this pendulum can be used to be a counting device.

7.0 Conclusion

1. The longer the length of string, the longer the time to make 1 complete oscillation. This is due to the farther distance of the pendulum to travel to complete oscillation.

2. The more weight added, the longer the time taken to make 1 complete oscillation. This is due to the more inertia of the pendulum to start the oscillation.

3. In short, both length and mass effect the time taken to make 1 complete oscillation.

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