# the pendulam

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Introduction

Parvez Patel

11 .4

Science

Mr Atwood

Course work

Investigation on Pendulum

Aim:

In this investigation I will explore how the varying length of a string affects the period of oscillation and a pendulum. I will further try to investigate if the period of oscillation is proportional to the length of the pendulum.

Prediction

I predict that if I increase the length of the string then the total time period will increase because from my background knowledge I know that the period of the pendulum is directly proportional to the length. So if I increase the length of the string them the time period of the pendulum will automatically increase.

Background knowledge

I made this prediction because when the length of the sting increases the speed of the pendulum moves quicker to do 10 oscillations. Whilst altering the length of the string this affects the pendulum because it makes it do 10 oscillations quicker when at 10 cm long, but when it’s at 100 cm long it takes longer.

Ideally a simple pendulum is a point mass on a light, inelastic string. In real experiment we use a pendulum bob of finite size.

Middle

O= because pendulum does not oscillates where there is no length.

Equipment Apparatus

Metallic bob

Stopwatch

Clamp

String

Ruler (100cm)

Variables

- It was fair test by keeping the height from which the pendulum has drop to same
- The dependent variable was measured for the time taken
- There’s an error in the stopwatch when timing
- When the string gets shorter the speed of the pendulum gets faster to do 10 oscillations.

Method

- I will firstly set up a clamp stand with a piece of string50 cm long attached to it
- A mass of 50g will be attached securely to the other end of the string
- The mass will be held to one side at an angle of 45degrees (measured with a protractor) and then released.
- A stop watched will be used to take time for oscillation
- This will be repeated a number of times, each time shortening the length of string by 10cm
- The length of the pendulum will be plotted against the period on a graph. The final length of string and mass will be decided after my preliminary investigation.

Apparatus

- Meter ruler
- Protector
- Clamp stand
- G-clamp
- Stop clock
- String
- Mass

The following factors will be considered when providing a fair test

- The mass will be a constant of 50g throughout the experiment
- Angle of amplitude shall be a constant of 45 degrees. This will ensure that there is no variation of the forces acting on the pendulum.
- The value of gravitational field strength will inevitably remain constant, helping me to provide a fair test.
- The intervals between the string lengths will increase by 10cm each time, This will help me to identify a clear pattern in my results
- If any anomalous results are identified, readings will be repeated. This will ensure that all the are sufficiently accurate

The following Factors are considered when providing a safe test.

- Care will be taken not to let the bob come into contact with anything whilst swinging the pendulum, as the weight is relatively heavy.
- The clamp stand will be firmly secured to the bench with G-clamp so that the clamp stand, will not move, affecting the results.
- Excessively large swings will be avoided ( angle of amplitude will be 45 degrees results of preliminary investigation):

Length of string (cm) Period (seconds)

50 2.58

40 2.31

30 2.11

20 1.78

10 1.39

My preliminary investigation was successful. The results from my table back up my prediction that, as the length of the pendulum increases, the period increases.

I learned from my preliminary investigation that my processed method might not give me a sufficient accurate result. These results may be inaccurate due to the slight error of measurement in time, height or length. I will also measure the time taken for 10 oscillation rather than 1 and divide the result the by 10. These two changes will hopefully help me to identify and eliminate anomalies, should they occur. They should also add to the accuracy of my results.

Obtaining Evidence

I used the method proposed in plan, taking three other readings of each value and measuring the time for 10 oscillations rather than for 1. During the experiment, I observed that each oscillation for the same length of the string seemed to be equal. This showed that the pendulum did not slow down as the number of oscillation increased. I took the safety measures described in my original plan.

During the experiment I was careful to use accurate measurements in order to obtain sufficiently accurate results, for example:

- The string was measured with a meter ruler , to nearest mm , to insure that each measurement had a difference of exactly 10cm
- The angle of amplitude will be measured with a protector to the nearest degree to ensure that the angle remains constant throughout the experiment.
- A stop clock will be used to measure the period accurately. The period was measured in second with the stop clock measuring to the degree of two decimal place in second. However I have rounded each time to the nearest second to give appropriate result.
- The mass was measured using five 10g masses, to ensure that the mass remain constant throughout the experiment.

Conclusion

361

70cm

18 seconds

324

60cm

17 seconds

289

50cm

15 seconds

225

40cm

13 seconds

169

30cm

11 seconds

121

20cm

9 seconds

81

10cm

7 seconds

49

This result came from the second time I did the experiment but this time I used this formula this is because I would know if I had done my experiment correctly and to see if I had any anomalous result.

Analysis

Using the results from my table, I drew the graph to show what had been obtained from the experiment. The graph clearly shows a smooth curve with a positive gradient. This indicates that as the length of the pendulum is increased.

Although my second graph does not show a perfect straight line through the origin, a line of best of fit can be drawn to show this. This backs up the theory in my scientific knowledge, that P is directly proportional to L, I.E. if the length of the string was doubled, the period will be doubled. My table of results drawn from my experiment was extremely similar to the results produced from my scientific formula, showing that my experiment was successful. My two Graphs showed resemblance to my predicted graphs. Indicating that my results were sufficiently accurate and therefore, my proposed method was reliable for this experiment.

My findings indicate that the time period varies directly with the length of the string when all factors remain constant

This student written piece of work is one of many that can be found in our GCSE Forces and Motion section.

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