To Find Effective Length of Seconds Pendulum Using Graph

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Introduction

In this experiment, you can determine the effective length of pendulum with the help of graphs. You should plot two types of graphs, such as L-T and L-T2 graphs.

All you need is a simple pendulum graph. Calculation of effective length is a very significant and sensitive experiment. Students should go for the error-free values to determine the right parameter at the end.

This article is completely based on simple pendulum experiment readings and graph. Students can gain a brief idea about this experiment after reading the article.


Materials or Apparatus Required

Some of the materials that are listed below for the second’s pendulum experiment:

  • Split Cork

  • Clamp stand

  • Long and strong cotton thread

  • Heavy metallic spherical bob with a hook

  • Meter scale

  • Graph Paper

  • Stopwatch

  • Pencil Eraser

Principle of Simple Pendulum Experiment

This experiment has the objective to find the time of a simple pendulum. Also, the length of the second’ pendulum can be calculated within the same operation. Simple harmonic motion on a simple pendulum exhibits an acceleration

As you know, the acceleration of the pendulum’s bob is directly proportional to the displacement from the mean position. The time is the value that we need to determine for the simple pendulum.

The relation of time is given below:

T = 2π √(L/G)


Procedure

  1. Keep the clamp stand over the table. Attach the pendulum bob with a hook. The length of the string is about 150 cm. another string is two half-pieces of a split cork.

  2. Attach the cork tightly with the clamp. This allows a better line of separation between the two pieces of the split cork at right angles to the line OA. When the pendulum oscillates, you can notice the change.

  3. Identify the edge of the table that the pendulum is reaching. Mark the lines that lie beyond the edge of the table (about 2 cm above the floor). Mark the line that comes just behind the vertical thread OA.

  4. After the setup, you can measure the length of the simple pendulum.

  5. Students must consider some of the effective length L along the x-axis. Also, consider the y-axis of value T2 (or T) for plotting the graph. Some of the experiential values from the table are taken into consideration. 

  6. Choose convenient scales on these axes to present L and T2 (or T). A graph that is plotted between L and T2 and also between L and has the impact.

[Image will be Uploaded Soon]


Observation

From the above setup, students should verify the details and answer the following parameters to get appropriate outputs. The following points are given for considering them:

  • Length of the hook = __ cm

  • The pendulum's radius of the bob = __ cm

  • The least count of the stopwatch = __ s

  • The least count of the meter scale = __ mm

S. No

String length from the top of the bob to the point of suspension 

Effective length,

L = (l+r+e)

Number of oscillations counted, n

Time for n oscillations t (s)

Period

T (= t/n)



cm

m


1

2

3

Mean t (s)





How to Plot the Graphs?

The simple pendulum graph is here as shown:

[Image will be Uploaded Soon]


i) L Vs T Graph

You can plot the graph between L~T to observe different outputs. A table can be helpful to note down all outputs. You can take L along the x-axis and T along the Y-axis. From the figure, you can notice that the graph will give you a curve line.


ii) L Vs T2 Graph

You can plot the graph between L and T3. All of the results can help you further if you keep them in a tabular form. The output of the relation will give you a straight line, as shown in the figure.


iii) We can find out the effective length of the second’s pendulum for T2 = 4s2 obtained from the second graph.


The Output of the Experiment

From the above experiment, you can obtain three output which is given below:

A curve that comes out of the L-T graph gives rise to convex upwards.

A straight line is obtained from the L – T2 graph.


Viva Questions

1. How Do You Define the Connection Between Frequency and Time?

Answer: The connection between frequency and time period is given by the following expression,

 f = 1/T


2. How Do You Define the Restoring Force?

Answer: Restoring force is a force that helps to bring back the vibrating body towards the mean position.  This force acts as the resistance force for the body that vibrates.


3. Is it Useful to Use a Cricket Ball Instead of the Bob in a Pendulum?

Answer: No, this is not that good. The bob must be lighter and smaller. A cricket ball can’t be the possible reason for the replacement period.


4. Why Don’t We Use a Rubber Band by Replacing the Thread?

Answer: No, this is not the way we should experiment. The rubber band is not inextensible like a thread. So, we keep the thread on a priority basis.

FAQ (Frequently Asked Questions)

Q1. Why Do We Use the Word ‘Simple’ for the Simple Pendulum?

Ans: Students know that the word ‘simple’ is associated with the pendulum. It is having a mass m attached with a string of length l. The string is fixed at a pivot point called P. 

The simple term is used for a simple pendulum because of the following parameters. It has a mass and is active. You must have seen the use of pendulums on the wall clocks. All of them are considered compound pendulums as they have a metallic string in place of a thread.

Q2. How Do You State Simple Harmonic Motion (S.H.M)?

And: We name a motion as a simple harmonic motion when it satisfies these following reasons:

(I) The acceleration’s magnitude is directly proportional to its displacement (from the mean position). 

(ii) The acceleration is always pointing to stay in the direction of its mean position.

Q3. What Do You Mean By a Pendulum?

Ans: A pendulum is an object attached to a string and swings back and forth because of gravity's presence. Pendulums are widely used among the wall-clocks and help them to regulate their movement.