Investigating the Period of oscillation of a Simple Pendulum

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Investigating the Period of oscillation of a Simple Pendulum

Investigating factors which affect the period time of a simple

pendulum

Planning

A simple pendulum is a mass suspended from a string, which is free to move and swing. When it is displaced from its central equilibrium position, by pulling the pendulum to one side and then releasing it. It will the swing from side to side in a repetitive movement, this is called an oscillation. The time taken to move from one side to another is called the Period.

In this investigation, I am going to experimentally determine a factor either length of the pendulum mass of the bob or the angle of displacement, which

will affect the period of a simple pendulum and the mathematical relationship of this factor. This type of pendulum will consist of a mass hanging on a length of string.

Factors, which affect the period (T) of a pendulum:

- Length (L) of pendulum

- Angle of amplitude

- Gravitational field strength (g)

- Mass of bob

I predict that the period will be affected by the length and only the length of the pendulum. An increase in length will produce an increase in time. I based by prediction on the scientific theory I found in a physics textbook:

The pendulum is able to work when the bob is raised to an angle larger than

the point at which it is vertically suspended at rest. By raising the bob, the

pendulum gains Gravitation Potential Energy or GPE, as in being raised, it is

held above this point of natural suspension and so therefore is acting against

the natural gravitational force. Once the bob is released, this gravitational

force is able to act on it, thus moving it downwards towards its original

hanging point. We can say therefore, that as it is released, the GPE is

converted into Kinetic Energy (KE) needed for the pendulum to swing. Once

the bob returns to its original point of suspension, the GPE has been totally

converted into KE, causing the bob to continue moving past its pivot point and up to a height equidistant from its pivot as its starting point.

The same factors affect the pendulum on its reverse swing. GPE gained after

reaching its highest point in its swing, is converted into KE needed for it to

return back to its natural point of vertical suspension. Due to this continuous

motion, the bob creates an arc shaped swing. The movement of the pendulum is repeated until an external force acts on it, causing it to cease in movement. The pendulum never looses any energy; it is simply converted from one form to another and back again.
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I am therefore going to experimentally determine the relationship between the length of the pendulum and the period.

In the scientific theory, I found a formula relating the length of the pendulum to the period. It stated that:

P = 2L

g

P = The period

g = Gravitational Field Strength

L = Length of string

This formula shows that L is the only variable that when altered will affect the value of P, as all the other values are constants.

The formula: P = 2Lg.

can ...

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