Simple Pendulum and Restoring Force

In the previous chapters we studied the motion of a body moving with uniform speed in a straight line and also learnt to calculate the distance traveled by a body in any given time. We then observed that the bodies do not always move with uniform speed and an external unbalanced force is responsible for producing acceleration in moving objects. This led to the study of the motion of accelerated bodies. Motion in a straight line with constant speed and constant acceleration is not the only kind of motion we come across in daily life. There is a kind of motion due to which a body moves to and fro about the mean position.

Examples:

The motion of the pendulum of a clock.

Motion of a swing.

Sub Topics

The Simple Pendulum

The Simple Pendulum

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A simple pendulum consists of a heavy mass (spherical in shape) suspended by a long weightless, inextensible and flexible string from a point about which it can oscillate. The mass which is attached to the end of the string is called the bob of the pendulum. The pendulum is suspended as shown in the figure.

A Simple pendulum

The position B where the simple pendulum rests is called the mean position of the simple pendulum. If the simple pendulum is displaced from its mean position (OB) to position (OC) and then released, we observe that the simple pendulum begins to move towards the mean position (OB) and then to extreme position (OA) and back to (OC) through (OB). Thus the bob of the simple pendulum keeps moving to and fro between the two extreme positions A and C about the mean position (OB). Such a to and fro motion which repeats itself at regular intervals of time about the mean position is called an oscillatory motion or harmonic motion. When the bob of the pendulum moves from one extreme position say A, to the other extreme position C and then back to the extreme position A, then we say that the simple pendulum has executed one oscillation or one vibration.

The time taken by the simple pendulum to execute one complete oscillation is called its Time period (T).

The length of the simple pendulum (L) is the distance from the point of suspension to the bob.

The distance covered by the bob from the mean position to an extreme position is called the amplitude of the pendulum. Now the question is how to find the time taken for one oscillation since it is very difficult to note the time for one oscillation. We generally measure the time taken by a large number of oscillations say n oscillations. Then the time period of the pendulum T is given by the relation,