Simple pendulum on Earth

SIMPLE PENDULUM ON EARTH

INTRODUCTION

Our Earth is the third planet in our solar system. Consider a simple pendulum on the surface of Earth ready to swing. A pendulum is a weight suspended from a pivot so that it can swing freely. It has a bob [mass] suspended from a frictionless pivot via a string. The central position of the bob i.e. when the pendulum is at rest is called its Mean position. When the bob is made to swing on the application of external force, it oscillates back and forth about this mean position. The maximum distance traversed by the bob from the mean position is known as amplitude. The amplitude is measured in radians which is a unit of angle. The time taken by the pendulum to complete one full oscillation is called the Time Period. For small amplitude less than 1 radian, the time period is independent of amplitude of the pendulum. We intend to determine the time period of such a pendulum on Earth.

A simple pendulum

ASSUMPTIONS

1. The string has no tension or compression

2. The pendulum is indestructible

3. Air resistance is negligible

4. Effect of Gravitational Time dilation is negligible

CALCULATION

The time period of a simple pendulum is given by,

T = 2π*√ (l/g) (Eqn. 1)

Where,

T – Time period [s]

l – Length of the pendulum [m]

g – Acceleration due to gravity on Earth [m/s²]

g = 9.8 m/s² (Eqn. 2)

Let the length of pendulum be

l = 1 m (Eqn. 3)

Now substitute equations (2), (3) in equation (1)

T = 2π*√ (1/9.8)

T = 2π*√ (0.1020)

T = 2π*0.3194

T = 2.007 s (Eqn. 4)

This is the time period of a simple pendulum on Earth. It means any pendulum performing small oscillations will always take approximately 2 second to complete one cycle anywhere on Earth provided the value of gravity is same everywhere and the effects of friction are neglected.

CONCLUSION

We thus determined the time period of a simple pendulum on Earth.