Aim: To investigate the factors that affect the time period of a pendulum

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Aim:

To investigate the factors that affect the time period of a pendulum.

Introduction:

A pendulum is a simple piece of equipment, A simple pendulum, is a weight on the end of a piece of string or wire, which when given an initial push, will swing back and forth under the influence of gravity.

The pendulum was discovered by Ibn Yunus al-Masri during the 10th century, which was the first person to study and document its oscillatory motion.

This diagram shows a simple pendulum and the path that it swings in.

The time period of a pendulum is the amount of time it takes to complete one full oscillation. I need to investigate the factors that effect one full oscillation in the pendulum. After I have done this I can decide which factors to keep the same and which factors to investigate.

Factors affecting the oscillation of a pndulum:

Length of string

The length of the string will affect the oscillation of a pendulum because it means that the pendulum will travel a greater distance in its oscillation. The path at the bottom of the pendulum is like an arc of a circle, with the piece of string a radius. Then according to the circle theorem: C=2πr the circumference will increase as the radius increases. As the circumference increases the bigger the displacement will be from the starting point and the longer the pendulum will take to return to its starting point.

Angle from which the pendulum is dropped

This affects the time period in two ways. The first is that it increases the length of the arc of the circle that I talked about earlier. The bigger the angle the bigger the proportion of the circle is taken up by the arc. More of the 360o of the circle are taken up meaning there is a bigger displacement in the oscillation. This in turn increases the time taken for an oscillation.

The second affect that the angle of release has is on the gravitational potential energy. If you increase the angle of release you are releasing it from a greater height and therefore increasing the gravitational potential energy.

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Gravitational potential = Mass x Gravity x height

Energy

So as you can see from this equation if you keep gravity and mass constant and increase the height you will increase the gravitational potential energy.

From another equation we can see how G.P.E will effect the oscillation.

Kinetic energy = Half x mass x velocity2

G.P.E = Kinetic energy

Mass x gravity x height = half x mass x velocity2

So from these equations you can see that as you increase G.P.E you will in turn increase the kinetic energy. This means that the pendulum will swing faster as the ...

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