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Investigate the factors which affect the time period of a simple pendulum.

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Introduction

aim of this coursework

In this coursework I intend to investigate the factors which affect the time period of a simple pendulum.

introduction

  A simple pendulum is made up of a small, dense and spherical object called a bob, connected to a thin inextensible wire which is attached to a rigid surface. A diagram of a pendulum is shown below:

image00.png

When disturbed from its state of rest the pendulum will oscillate about its rest position. For a simple pendulum one complete oscillation is one complete ‘to-and-fro’ motion. There are three types of oscillations:

  • FREE: The body oscillates with no external force acting on it.
  • DAMPED: Oscillation is influenced by the frictional force of the medium.
  • FORCED: Oscillation is influenced by a constant external force.

On earth the pendulum is a damped oscillating body due to air resistance but in my coursework I will ignore this effect and consider the pendulum as a freely oscillating body.

...read more.

Middle

image04.png

forces acting on the pendulum

At rest position, there are two forces acting on the bob: the tension of the string on the bob acting upwards and the weight of the bob acting downwards. At rest position, these two forces act equal and opposite to each other (Newton’s Third Law of Motion) and so the pendulum is at equilibrium i.e. there is no overall change or effect.

image05.png

However, when disturbed there is a change:

image06.png

As shown in the diagram, the forces are equal but not opposite. Therefore there is a resultant force acting on the pendulum, which causes it to oscillate. In order to understand how the resultant force is brought about, I will resolve the force exerted by the weight of the bob into its components.

  A force acting in one direction can be resolved into two mutually perpendicular components.

...read more.

Conclusion

  However, when it does reach the rest position the bob will not stop. Instead it will continue to ‘swing’ to the other side. This is because of inertia – the reluctance of a body to stop moving while it is in motion. It will continue to move to the other side and the process repeats, causing the pendulum to oscillate.

energy changes taking place during oscillation

image03.png

At the rest position R the bob is at its minimum height from the ground. When the pendulum oscillates the height varies at different points. In the diagram A and B are at maximum height considering the height from position R as a reference. Since gravitational potential energy also depends on height, the pendulum gains maximum gravitational potential energy at positions A and B.

  The gravitational potential energy is the product of the mass of the bob by the gravitational field strength of earth by the height of center of the bob from the reference level i.e. its height from the center of the bob during rest position.

...read more.

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