A presentation on Simple Pendulum - important terms and relationships between time period and frequency and time period and effective length and acceleration due to gravity

1. INTRODUCTION
Do some of you have this
at home?
What do we call this?
It is called a Grandfather
Clock
Please pay attention to the portion
circled

2. INTRODUCTION
Do some of you have this
at home?
What do we call this?
It is just a Wall Clock
Again pay attention to the portion
circled

3. INTRODUCTION
In both the images, what
were the portions circled?
It is the Pendulum
What is the role of the
pendulum?
It keeps the time of the
clock

4. SIMPLE PENDULUM
CLASS IX

5. SIMPLE PENDULUM
DEFINITION
A simple pendulum is a heavy point mass (known as
bob) suspended from a rigid support by a massless
and inextensible string
PROPERTY
The periodic oscillations of the pendulum in a
pendulum clock keeps the time in it

6. SIMPLE PENDULUM
Note:
1. A heavy mass with the size of a point is not
possible
2. A massless string is also impossible
So the definition is more an ideal but not altogether
a real world situation

7. OSCILLATION One complete to and fro motion of the bob of the
pendulum is called one Oscillation
TERMS RELATED TO A SIMPLE PENDULUM
AMPLITUDE The maximum displacement of the bob from its mean
position on either side is the Amplitude of oscillation. It is
denoted by ‘a’ or ‘A’ and measured in metre (m)
TIME PERIOD or
PERIOD OF
OSCILLATION
The time taken to complete one oscillation is called the
Time Period or Period of Oscillation. It is denoted by ‘T’ and
its unit is second (s)
FREQUENCY of
OSCILLATION
The number of oscillations made in one second is called
the Frequency of oscillation. It is denoted by ‘f’ or ‘n’ and its
unit is hertz (Hz) or (s-1)

8. EFFECTIVE
LENGTH of a
SIMPLE
PENDULUM
The distance of the point of oscillation (that is, the centre of
gravity of the bob) from the point of suspension is called
the Effective Length of the Simple Pendulum
TERMS RELATED TO A SIMPLE PENDULUM

9. SUMMARY OF TERMS
O is the mean position and
A or B are extreme positions
O to A or O to B is the
amplitude
Effective length
One oscillation is movement from O to A,
A to B and then from B back to O

10. RELATION BETWEEN TIME PERIOD AND
FREQUENCY
FREQUENCY
TIME PERIOD

11. MEASUREMENT OF TIME PERIOD OF A SIMPLE
PENDULUM
1. We slightly displace the bob of a simple pendulum from the
mean position and release the bob
2. We then measure the time (t) for 20 oscillations with the help of
a stop clock
3. Time (t) divided by 20 gives us the time period (T)
4. The experiment is repeated for pendulums of different length
5. The observations are then recorded as in the table in the next
slide

12. MEASUREMENT OF TIME PERIOD OF A SIMPLE
PENDULUM
𝒍
𝑻𝟐 is the same for different lengths of the pendulum and is a constant

13. MEASUREMENT OF TIME PERIOD OF A SIMPLE
PENDULUM
When the length of the
pendulum is increased four
times, the time period gets
doubled

14. GRAPH FOR VARIATION OF SQUARE OF TIME PERIOD
(T2) WITH LENGTH (l)OF A PENDULUM
When we plot the T2
against l we get a straight
line graph

15. GRAPH FOR VARIATION OF SQUARE OF TIME PERIOD
(T2) WITH LENGTH (l)OF A PENDULUM
𝑺𝒍𝒐𝒑𝒆 𝒐𝒇 𝑷𝑸 =
𝑷𝑹
𝑸𝑹
=
𝒂𝒃
𝒄𝒅
=
𝑻𝟏
𝟐
− 𝑻𝟐
𝟐
𝒍𝟏 − 𝒍𝟐
𝒈 =
𝟒𝝅𝟐
𝑺𝒍𝒐𝒑𝒆 𝒐𝒇 𝑻𝟐 𝒗𝒔 𝒍 𝒈𝒓𝒂𝒑𝒉

16. FACTORS AFFECTING THE FREQUENCY OF A SIMPLE
PENDULUM

17. FACTORS AFFECTING THE TIME PERIOD OF A SIMPLE
PENDULUM
1. The time period of oscillation of a simple pendulum is directly
proportional to the square root of its effective length
𝑻 ∝ 𝒍 or 𝑻𝟐 ∝ 𝒍
• In a pendulum clock, the pendulum is made of a metal such as brass or steel
• In summer it expands and the effective length increases, increasing the time period
(less number of oscillations in a give time, i.e., clock goes slow)
• In winter it contracts and the effective length decreases, decreasing the time
period (more number of oscillations in a give time, i.e., clock goes fast)

18. FACTORS AFFECTING THE TIME PERIOD OF A SIMPLE
PENDULUM
2. The time period of oscillation of a simple pendulum is inversely
proportional to the square root of acceleration due to gravity
𝑻 ∝
𝟏
𝒈
• Thus a pendulum clock goes slow when taken up on the mountains or down into
the mines (i.e., time period of oscillation decreases)
• Acceleration due to gravity (g) decrease with altitude and depth

19. FACTORS AFFECTING THE TIME PERIOD OF A SIMPLE
PENDULUM
3. The time period of oscillation of a simple pendulum does not depend
on the mass or material of the suspended mass (bob)
• If we take two pendulums of equal length but bobs of different mass or material,
the time periods remain the same

20. FACTORS AFFECTING THE TIME PERIOD OF A SIMPLE
PENDULUM
4. The time period of oscillation of a simple pendulum does not depend
on the extent of swing on either side (i.e., amplitude)
• This holds as long as the swing is not too large (not greater than 15°)

21. EXPRESSION FOR THE TIME PERIOD OF A SIMPLE
PENDULUM
The time period of oscillations of a simple pendulum is given by
• T = time period
• l = effective length of pendulum (l+r)
• g = acceleration due to gravity
𝑻 = 𝟐𝝅
𝒍
𝒈
or 𝑻𝟐 = 𝟒𝝅𝟐 𝒍
𝒈