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.

Simple pendulum on International Space station

SIMPLE PENDULUM ON ISS

INTRODUCTION

The International Space Station [ISS] is a satellite orbiting earth at approximately 250 miles from the surface. Consider a pendulum aboard the ISS. 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 ISS. The ISS is always in a state of free fall hence all objects inside ISS will experience weightlessness.

A simple pendulum

ASSUMPTIONS

1. The string has no tension or compression

2. The pendulum is indestructible

3. Air resistance 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 ISS [m/s²]

g = 0 m/s² {due to free fall} (Eqn. 2)                 

Let the length of pendulum be

l = 1 m (Eqn. 3)

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

T = 2π*√ (1/0)

T = 2π*√ (∞)

T = 2π*∞

T = ∞ s (Eqn. 4)

This is the time period of a simple pendulum on ISS. This clearly indicates that Time period does not exist for the pendulum inside ISS. Even when a small force is applied to the bob, the bob will just move in one direction and never return to the mean position due to lack of gravity.

CONCLUSION

We thus concluded that the pendulum will not work aboard the ISS due to lack of gravity.

Simple pendulum on Sun

SIMPLE PENDULUM ON SUN

INTRODUCTION

Sun is our star in the center of our solar system. Consider a fire resistant pendulum on the surface of Sun 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 Sun.

A Simple Pendulum

ASSUMPTIONS

1. The string has no tension or compression

2. The pendulum is indestructible and it is immune to destruction by gravity, high temperature or solar winds

3. Air and wind resistance are 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 Sun [m/s²]

g = 273.7 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*√ (1/273.7)

T = 2π*√ (3.6536*10^-3)

T = 2π*0.0604

T = 0.3797 s (Eqn. 4) 

This is the time period of a simple pendulum on Sun. It means any pendulum performing small oscillations will always take approximately 1/3 second to complete one cycle anywhere on Sun provided the value of gravity is same everywhere and the effects of friction are neglected. Due to high gravity of Sun, the time period is extremely small, way smaller than that on Earth and Jupiter.

CONCLUSION

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

Arduino Airplane Lights

ARDUINO AIRPLANE LIGHTS

INTRODUCTION

This is an Arduino DIY project intended to simulate airplane lights. Airplanes are detectable in the night sky solely because of their lights. Most airplanes have three lights, one at the bottom and other on edge of each wing. The most common configuration is one red light at the bottom and two white lights on the wing.

COMPONENTS REQUIRED

1. Breadboard

2. Arduino UNO

3. One 5mm Red LED

4. Two 5mm White LED’s

5. Three 20 Ohm resistors

6. Breadboard jumpers (wires)

CIRCUIT SCHEMATICS

Make the appropriate connections as shown in the schematic above

CODE

This is the code for simulating Arduino Airplane lights. Copy and paste the code in Arduino IDE sketch area. Note that the values and choice of ports can always be changed.

void setup() {

  // put your setup code here, to run once:

pinMode(4, OUTPUT); //Red LED

pinMode(7, OUTPUT); //White LED

pinMode(8, OUTPUT); //White LED

}

void loop() {

  // put your main code here, to run repeatedly:

digitalWrite (4, HIGH);

delay(500);

digitalWrite(4, LOW);

delay(200);

digitalWrite (7, HIGH);

digitalWrite (8, HIGH);

delay(100);

digitalWrite(7, LOW);

digitalWrite(8, LOW);

delay(300);

}