Poha Lab

SIMPLE PENDULUM:

A simple pendulum is a point mass suspended by a weightless and inextensible string fixed rigidly to support.

EXPLANATION

A simple pendulum is a mechanical arrangement that demonstrates periodic motion. It comprises a small bob of mass ‘m’ suspended by a thin string secured to a platform at its upper end of length L. This system sways or moves in an oscillatory motion. This motion occurs in a vertical plane and is mainly driven by gravitational force. Interestingly, the bob that is suspended at the end of a thread is very light; somewhat, we can say it is even massless. The period of a simple pendulum can be made extended by increasing the length string while taking the measurements from the point of suspension to the middle of the bob. However, it should be noted that if the mass of the bob is changed, the period will remain unchanged. The period is influenced mainly by the position of the pendulum in relation to Earth, as the strength of the gravitational field is not uniform everywhere.

In addition, pendulums are a common system whose usage is seen in various instances. Some are used in clocks to keep track of the time, while some are just used for fun in case of a child’s swing. In some cases, it is used in an unconventional manner, such as a sinker on a fishing line. In any case, we will explore and learn more about the simple pendulum, and as well as We will derive an interesting expression for its period.

IMPORTANT TERMS:

The oscillatory motion of a simple pendulum: Oscillatory motion is defined as the to and fro motion of the pendulum in a periodic fashion, and the center point of oscillation is known as the equilibrium position.
The time period of a simple pendulum: It is defined as the time taken by the pendulum to finish one full oscillation and is denoted by “T”.
The amplitude of a simple pendulum: It is defined as the distance traveled by the pendulum from the equilibrium position to one side.
Length of a simple pendulum: It is defined as the distance between the point of suspension to the center of the bob and is denoted by “l”.

EXPRESSION FOR TIME PERIOD OF SIMPLE PENDULUM:

The mathematical expression for time period of simple pendulum is:
T=2π√l/g
This equation shows that time period pendulum depends on the length of a simple pendulum and the acceleration due to gravity with no direct dependence on the mass of the bob. However, experimental verification is necessary to confirm this relationship.

APPARATUS

Two identical bobs of different masses with hooks
Thread/ an inextensible string.
Iron stand with clamp and heavy base.
Vernier caliper
Stopwatch
Metre rule
Laboratory balance.
Calculator
Piece of chalk

Procedure

Find the mass of each bob with the help of laboratory balance.
Measure the diameter of the hook of the bob with the help of a Vernier caliper and calculate the radius of the bob (i.e. D/2)
Take an inextensible string and tie its one end with the hook of the bob.
Place the other end of the string between the split corks.
Clamp the cork on an iron stand. The bob of a pendulum must be a few cm above the ground.
Measure the length of the string including the hook. The total length of the pendulum will be l=l+r.
Draw two mutually perpendicular lines with the help of the chalk on the floor mean position o, point A and point B shows extreme position A and B.
Then release the bob gently. The oscillation of the bob should be along a straight line.
Start the stopwatch when the bob just passes point o and at the same time start counting the oscillations from zero. Note the time for 2D complete oscillation.
Repeat step 8 to obtain another value of time t2 and find the mean t, t=(t1+t2)/2.
Calculate the mean time period for one oscillation as, T=t/10.
Calculate the time period for each bob and record them. Results will show that the time period for each bob remains the same.

PRECAUTIONS

The thread should be very light and strong.
The point of suspension should be reasonably rigid.
The pendulum should oscillate in the vertical plane without any spin motion.
The floor of the laboratory should not have vibration, which may cause a deviation from the regular oscillation of the pendulum.
The length of the pendulum should be as large as possible in the given situation.’
Determination of time for 20 or more oscillations should be carefully taken and repeated at least three times.
There must not be a strong wind blowing during the experiment.

Viva Questions

Q1. What is an expression for the time period of a simple pendulum?

Q2. On what factors does the energy of the particle executing S.H.M. depend?

Q3. What is a second’s pendulum?

Q4. When will the motion of a simple pendulum be simple harmonic motion?

Q5. Will the time period increase or decrease when a pendulum is taken on top of the mountain?

Q6. Why does a simple pendulum not vibrate at the center of the earth?

Q7. A vibrating simple pendulum of time period T is placed in a lift which is accelerating upwards. What will be the effect on the time period?

MCQ's

1. Simple Pendulum does not vibrate at.

North Pole.

South Pole.

Surface of the earth.

Center of the earth.

2. When a pendulum is taken on the top of the mountain, the time period will:

Increase

Decrease

Remain constant.

Become zero.

3. The velocity of a particle moving with simple harmonic motion is __________ at mean position.

Zero

Minimum

Maximum

None of the above.

4. When a rigid body is suspended vertically and it oscillates with a small amplitude under the action of the force of gravity, the body is known as:

Simple pendulum.

Second’s pendulum.

Torsional Pendulum.

Compound Pendulum.

5. Which one of the following laws is not applicable to a simple pendulum?

The time period depends on its amplitude.

The time period is proportional to the length ‘l’ of the pendulum.

The time period is proportional to the acceleration due to gravity ‘g’.

None of the above.

6. A girl sitting on a swing. Another sits by her side. What will be the effect on the time period of the swing.

Increase

Decrease

No effect.

None of these.

7. A Second’s Pendulum executes:

0.5 beats per second.

1.5 beats per second.

2.0 beats per second.

2.5 beats per second.

Physics

Prove that time period of a simple pendulum is independent of mass of the Pendulum