You might easily recall the big grandfather clock bearing a long stick with a ball attached at the bottom. It moved back and forth in harmony with every movement of the second hand. That was nothing but a pendulum.

Its motion is not only beautiful to witness but also has many scientific applications. Pendulum clocks and instruments like seismometers, accelerometers, and gravimeters all rely on this motion of a pendulum.

This content will help you understand how the pendulum works, its theory, and its experimental process, along with well-labelled diagrams.

### What is a Simple Pendulum, and how does it work?

**A simple pendulum comprises a metallic bob suspended via a weightless, inelastic and inextensible string attached to a fixed point**. In other words, a simple pendulum is a mass that remains hung through a hinge and allowed to swing back and forth in harmony.

Gravity serves the role of **restorative force** as soon as you displace the bob laterally from its mean point. This restoration force brings or accelerates the bob to come back to its equilibrium position. But the movement of the bob carries it past its equilibrium point. Thereby the direction of the restoring force changes in the opposite direction, directing the bob towards the mean position again.

Also, this force acting on the weight of the pendulum creates a cycle of motion or oscillations around its neutral position, including both left and right swings. The time interval required to complete one cycle varies as per the pendulum’s length by amplitude and breadth of swing.

### Simple Pendulum Experiment

A simple pendulum experiment is a set of apparatus that helps us to learn the working of the pendulum. Also, it helps to find out the associated concepts like oscillatory motion, time period of the pendulum, effect of change in the length of string etc.

## Content: Simple Pendulum Experiment

- Aim of Simple Pendulum Experiment
- Theory of Simple Pendulum Experiment
- Experimental procedure of Simple Pendulum Experiment
- Graphs of simple pendulum experiment
- Conclusion of Simple Pendulum Experiment
- Precautions for Simple Pendulum Experiment
- Frequently Asked Questions (FAQs)

### Aim of Simple Pendulum Experiment

1. To observe that the time period varies with the length of the string attached to the pendulum.

2. To find the acceleration due to gravity by plotting the L – T^{2} graph.

### Theory of Simple Pendulum Experiment

When the bob is at rest hanging in a straight line, it is in its mean position. When the bob displaces from that position, it begins to oscillate to and fro from one extreme to the other and then returns to equilibrium. This cycle of** A to B**, **B to C** and **C to A** goes on continuously until the bob comes to rest again. The simple pendulum produces synchronized oscillations exhibiting **simple harmonic motion (SHM)**.

The acceleration of the pendulum is directly proportional to its displacement from the equilibrium position. This implies that the more the displacement of the pendulum bob, the more its acceleration will be.

In general, the acceleration due to gravity at any point is given as:

Where,

g = Acceleration due to gravity

L = length of the pendulum

T = Time period of the pendulum

The time period of the pendulum is determined as the time taken to complete n oscillations divided by the number of oscillations(n). the pendulum varies with the length of the string.

### Procedure of Simple Pendulum Experiment

##### Aim 1: To determine the change in the time period with the gradual change of length of the pendulum.

- Take the stand with a clamp attached and suspend the bob to it with an inelastic, light thread.
- Adjust the length of the string to 50 cm from the point of suspension and the centre of the bob.
- Now, gently pull the pendulum bob from its mean position and swing it in such a way that the bob moves from the left extreme point to the right extreme point and then back to its mean. Count this as one complete oscillation.
- With the help of a stopwatch, record the time taken by the pendulum for completing 10 oscillations.
- Now calculate the time period by using the formula:

**Time period = Time take for 10 oscillations/ 10** - Repeat the same process by gradually changing the length of the string to 60 cm, 70 cm and 80 cm.
- Plot the graph between length and time period. (Time period (T) on the y-axis and length(L) on the x-axis.

##### Aim 2: To determine the acceleration due to gravity at a place by plotting L – T^{2}.

- Note down the diameter of the simple pendulum bob with the help of Vernier callipers.
- Tie the bob to one end of the string and pass the other end via two halves of the cork that is firmly fit in the clamp stand.
- Adjust the length of the pendulum string to 50 cm by using a ruler.
- Now, allow the pendulum to oscillate (making the angle less than 15
^{o}). - Start the stopwatch when the bob crosses its equilibrium position.
- Stop the watch when the oscillation count reaches 20 and note the time taken.
- Now calculate the time period by using the formula:

**Time period = Time take for 20 oscillations/ 20** - Repeat the experiment with different lengths of string as 60 cm, 70 cm and 80 cm.
- Calculate the value of L/T
^{2}in each case. (It is always a constant value). - Now estimate the value of acceleration due to gravity with the formula:

**g = 4𝛑**where;^{2}(L/T^{2})

g = Acceleration due to gravity

L = length of the pendulum

T = Time period of the pendulum - You can also calculate the g value by plotting the
**L – T**. Plot a graph with L along the x-axis and T^{2}graph^{2}along the y-axis. - From the graph, calculate the
**L/T**i.e.,^{2},**AB/OB.**

### Graphs of Simple Pendulum Experiment

#### Graph 1: L Vs T graph

This will be a curved graph as depicted in the image.

#### Graph 2: L Vs T^{2}

This will obtain a straight line as depicted below.

### Conclusion of Simple Pendulum Experiment

1. Graph 1 between L and T infers that the time period varies with the change in length of the pendulum.

2. Graph 2 between L and T^{2} determines the acceleration due to gravity at varying string lengths.

### Precautions

- The string or thread used should be completely inelastic, inextensible and weightless.
- The bob should not spin during the oscillations.
- The fans must be switched off to avoid any kind of fluctuations.
- The stopwatch used must give accurate readings.
- The metre scales used must be accurate so as to avoid measurement errors.

### Frequently Asked Questions (FAQs)

**What is simple harmonic motion?**

Regular to and fro movement of an object around its equilibrium position is termed simple harmonic motion.

**What does the word “simple” indicate in a simple pendulum?**

It is considered simple because it is a simple arrangement consisting of a mass hanging from an inelastic light-weighted thread. Whereas the ones in wall clocks and machines are the compound pendulums which use metallic or wooden stick in place of thread.

**What is restoring force in a simple pendulum experiment?**

It is the force that acts on the pendulum bob to bring it back to its mean position. For a pendulum, the gravitation force acts as a restoration force.

Pat says

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