Simple pendulum on Neutron star

SIMPLE PENDULUM ON NEUTRON STAR

INTRODUCTION

A Neutron Star is an extremely dense star formed after a Super nova explosion if the remnant mass is 3 to 5 solar masses. Consider an indestructible pendulum on the surface of a Neutron star 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 Neutron Star.

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 Neutron Star [m/s²]

g = 7*10¹² 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/{7*10¹²})

T = 2π*√ (1.4285*10^-13)

T = 2π*3.7796*10^-7

T = 2.3748 *10^-6 s (Eqn. 4)    

This is the time period of a simple pendulum on Neutron Star. It means any pendulum performing small oscillations will always take approximately 2 micro second to complete one cycle anywhere on Neutron Star provided the value of gravity is same everywhere and the effects of friction are neglected. Due to extreme gravity, the time period is really small, way smaller than that on Jupiter and Sun.

CONCLUSION

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