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Carry out an experiment of simple harmonic motion using a simple pendulum and determine the acceleration due to gravity.

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Introduction

SIMPLE HARMONIC MOTION AND THE SIMPLE PENDULUM

Task 1

Aim

To carry out an experiment of simple harmonic motion using a simple pendulum and determine the acceleration due to gravity.

Method

The apparatus is set up as above, the string must be measured accordingly with a ruler carefully to minimize any error.  The pendulum must be in equilibrium position which is central, where the pendulum does not move, as this gives more accuracy in timing the time period which is the time it takes for one complete oscillation.

The pendulum is put into movement by a gentle push, keeping the amplitude small, and the stopwatch is started.

Some practice counting and timing the oscillations may be needed to prepare for the experiment.

20 oscillations are counted and timing is stopped, it is then repeated to give an average time for the 20 oscillations and greater accuracy in the results.

The experiment is repeated 7 more times, with the length of string being increased by 0.1m.

...read more.

Middle

1.10

0.55

0.4

25.1

25.31

25.21

1.26

0.63

0.5

27.94

28.00

27.97

1.40

0.71

0.6

30.44

30.47

30.455

1.52

0.77

0.7

32.44

32.56

32.5

1.63

0.84

0.8

34.91

34.88

34.895

1.74

0.90

Analysis of Results

        The graph is time against length, so using the equation T = 2L/g

The gradient of the graph can be calculated from   ΔΥ    and is equal to  2ΔΧg

ΔΥ  = 1.18    = 1.98

ΔΧ     0.595

1.98 = 2  = 6.2

g      g

g =  6.2   = 3.13

        1.98

g = 3.13²

= 9.8ms²

Conclusion

        The value I obtained for the acceleration of the simple pendulum due to gravity is 9.8ms², which is good.  This shows that the experiment was accurate

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Conclusion

My graph has a straight line through the origin that does seem to be showing a pattern between the length and time.  As expected the time period increases as length of the pendulum is increased.  All my results are either very close or on the line of best fit showing that there were no serious errors in the experiment.

Task 2

Pendulums provide good time keeping because they perform simple harmonic motion and therefore can always have the same time period irrelevant of their mass.

Grandfather clocks have a time period of 2 seconds.

The length of the pendulum needed can be obtained from the following equation

T = 2L/m

2 = 2L/9.81

  2  = L/9.81

2

(0.32)² = L/9.81

  1. = L/9.81
  1. x 9.81 = L

L = 0.981 m

Task 3

To calculate the maximum amplitude of the oscillations if the mass is not to lose contact with the tray, first the time period must be worked out, by using the following equation.

T = 2m/k

T = 21.3/15Nm¹

T = 20.086

T = 20.3

T = 1.9s

...read more.

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