In this Coursework, we were given the task of investigating some factors which affect the period of a simple pendulum.

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INTRODUCTION:

A pendulum is a device which consists of an object suspended from a fixed point that swings back and forth under the influence of gravity. This effect is known as gravitation. However simple it may seem, this structure is very beneficial in our everyday life for it is used in several kinds of mechanical devices such as the all popular grandfather clocks. In addition to this, a pendulum could determine the local acceleration of gravity. This is the case, as the strength of gravity varies at different latitudes and as gravity is one of the main forces acting on the pendulum, the acceleration of gravity could be noted. Further uses of the pendulum are found in the field of astronomy for some have been used to record the irregular rotation of the earth as well as to detect earthquakes and others are used to demonstrate the rotation of the earth.

The pendulum and its applications were first discovered by Italian physicist and astronomer Galileo, who established that the period for the back-and-forth oscillation of a pendulum of a given length remains the same, no matter how large its arc, or amplitude. (If the amplitude is too large, however, the period of the pendulum is dependent on the amplitude.) This phenomenon is called isochronism.

A pendulum can be seen as a device whose energy is continually changing. When the pendulum swings to & fro, its energy changes from gravitational potential energy to kinetic energy and so on. This diagram of a simple pendulum clarifies this:

AIM:

In this Coursework, we were given the task of investigating some factors which affect the period of a simple pendulum. A period, is one complete oscillation. Possible factors that effect the period of a pendulum are:

- Mass of object suspended

2- Length of string

3- Angle.

However, due to limitations of time, and the complexity of carrying out some of the factors mentioned above, I will only look at 2 of the factors to investigate. They are:

- Length of string

2- Angle.

Before I give my predictions, I will give a brief outline for the experiments I shall be carrying out to allow the reader to understand my predictions.

- VARYING THE LENGTH: In this experiment, as the title suggests, I will be varying the length of the string the object is suspended from. The range will be between 0.1 M and 1 M & I will be going up in fixed intervals of 0.1 M. I will then measure the time it takes for 10 complete oscillations to occur at each length.

2- VARYING THE ANGLE: In this experiment, I will be varying the angle. The range will be between 10 & 80 degrees and I will be going up in fixed intervals of 10. I will then measure the time it takes for 10 complete oscillations to occur at each angle.

VARIABLES:

Before going on to explaining the experiments I will be devising in detail & my predictions, I must distinguish between three types of variables:

- INDEPENDENT VARIABLE: This can be considered as the input of the experiment. It is therefore deliberately changed, in order for us to see the effects of its change and obtain the results.

2-CONTROL VARIABLE: This is the factor which insures that the experiment is a fair test. It is always kept constant while the independent variable changes.

3- DEPENDANT VARIABLE: This can be considered to be the output of the experiment. It depends entirely, on the variation of the Independent variable.

In the experiment where I am varying the length, the variables are as follows:

Independent variable: The length of the string. I will be testing my experiment when the length of the string is at 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 & 1 metre.

Control variable: In order to maintain a fair test in this experiment, I shall control the following variables:

- The mass of the suspended object which is 21 grams.

2- The angle which will be 10 degrees.

Dependant Variable: The dependant variable is the time it takes 10 periods to occur.

In the experiment where I am varying the angle, the variables are as follows:

Independent variable: I will be testing my experiment when the angle is at 10, 20, 30, 40, 50, 60, 70 & 80 degrees.

Control variable: In order to maintain a fair test in this experiment, I shall control the following variables:

- The mass of the suspended object which is 21 grams.

2- The length of the string which will be 20 centimetres.

Dependant Variable: The dependant variable is the time it takes 10 periods to occur.

PREDICTIONS & THEIR EXPLANATION:

EXPERIMENT No. 1- VARYING THE LENGTH:

- As the length of the string increases, the period increases.

2- Their will be a proportional relationship between length of string & the period squared.

- As the length increases, the time taken for a period to occur will increase. This can very easily be justified by looking at the nature of arcs. As it is known, the object suspended from a simple pendulum moves from A to B through an arc. By increasing the length of the string, one side of the arc i.e. the radius increases and hence the object has to travel through a larger arc and a greater distance provided that the mass of the object and the angle remain constant.

The distance an object suspended from a pendulum travels to reach from A to B could be worked out. I will compare 2 situations where the length of the string varies and hence prove that the time taken for a period to occur will increase as the length increases.

Situation no. 1: When the length of string i.e. radius is 1 m and the angle is 10 degrees, we could use the formula X/360 * ?D, to work out the circumference of the arc. It will equal:

20 / 360 * ? * 2 = 0.35m

Situation no.2 : When the length of string i.e. radius is 2 m and the angle is 10 degrees, we could use the formula X/360 * ?D, to work out the circumference of the arc. It will equal:

20 / 360 * ? * 4 = 0.7m

The two situations prove that if the length of string (radius) increases, then the arc increases. i.e. the distance between A & B will increase. This will undoubtedly lead to an increase in the time it takes 1 complete oscillation to occur, and thus I could conclusively say that the period will increase as the length increases.
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2- Initially, I thought that there will be a proportional relationship between length of string & period because when looking at the two situations above, we find that when the radius - length of string - is doubled, the arc also doubles in length. Hence, I thought that the period will double as the distance of the arc will double when we double the length of the string.

After further reading to this topic, I found that this will not be true. This was discovered, after reading the formula which relates period of the pendulum to ...

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