# Simple Pendulum 3

```SCHOOL: UNIVERSITY OF LUSAKA
LAB REPORT: THE SIMPLE PENDULUM
NAMES AND STUDENT NUMBERS:
Brandon Panashe Beta PMBChB24122159
Ayanda Chiruo PMBChB23220251
Kalaba Chembe PMBChB23222026
Chipo Chikalipa PMBChB23221641
Taonga Banda PMBChB23220302
Esaya Banda PMBChB23221524
Malvern Chisiri PMBChB23221851
PROGRAM: BACHELOR OF MEDICINE AND SURGERY
(PRE-MED)
INTAKE: PMBCHB 1ST YEAR 1ST SEMESTER
INSTRUCTOR’S NAME: MR ANDERSON LUNGU
COURSE NAME: PHYSICS
COURSE CODE: (PMPH120)
CLASS SECTION: GROUP 1A
DUE DATE: 24/07/2023
LECTURER’S NAME: MR. M. ZULU
1.0 Abstract:
The experiment was carried out to show that the length of the pendulum influenced the
period of the oscillations. In the experiment the length was varied. The variables such as
angle of displacement, the mass of the bob and the number of oscillations (50) were kept
constant throughout the experiment. The experiment clearly showed that the length of the
pendulum had a direct relation with the period of oscillation.
2.0 Introduction:
The purpose of the experiment is to study the motion of a simple pendulum and to learn
the relationship between period, frequency, amplitude, and length of the simple pendulum.
The hypothesis of the experiment is if the period of the simple pendulum has a direct
relationship with the length of the pendulum. A simple pendulum consists of a bob
suspended by a light (massless) string of length ‘L’ fixed at its upper end. In an ideal case,
when a mass is pulled back and release, the mass swings through its equilibrium point to a
point equal in height to the release point, and back to the original release point over the
same path. The force that keeps the pendulum bob constantly moving towards the
equilibrium position is the force of gravity acting on the bob. The period ‘T’, of an object in
simple harmonic motion is defined as the time for one complete cycle.
3.0 Materials:
The following apparatus were used in this experiment: a meter stick, stopwatch, 125cm light
string, metal bob, string clamp, and the retort stand.
3.1 Methods:
A string of approximately 125cm in length was clamped by a string clamp between two flat
pieces of metal. The initial length of the pendulum was set at 0.10m. The length of the simple
pendulum is the distance from the point of suspension to the center of the ball. The pendulum
was displaced about 5 degrees from its equilibrium position and let to swing back and forth.
The total time it took to make 50 oscillations was then measured. The length was increased by
0.10m and the measurements were repeated until the length was approximately 1.0m. The
period of the oscillations for each length was found by dividing the total time by number of
oscillations, 50.
The results are clearly shown in the table below.
4.0 Results:
Length of pendulum
(m)
Time t, for 50
oscillations
(s)
Period T
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
31.0
44.0
53.4
62.7
71.1
77.5
83.7
89.0
93.0
99.0
0.62
0.88
1.07
1.25
1.42
1.55
1.67
1.78
1.86
1.98
(s)
Period squared (T2)
(s2)
0.38
0.77
1.14
1.56
2.01
2.40
2.78
3.16
3.45
3.92
The period increases as the length of the pendulum increases.
4.1 Graphical Analysis and Sample Calculations:
FIGURE 1
Length of pendulum against period
2.5
Period (S)
2
1.5
1
0.5
0
0
0.2
0.4
0.6
Length of pendulum (m)
0.8
1
1.2
FIGURE 2
Length of pendulum against period squared
4.5
4
3.5
period/s^2
3
2.5
2
1.5
1
0.5
0
0
0.2
0.4
0.6
Length of pendulum/m
0.8
1
1.2
Aco
5.Discussion:In
7.0 Discussion:
In the experiment carried out, the length (L) of the pendulum was the independent variable
whereas the time, period (T) of the pendulum was the dependent variable. While plotting the
graphs, the length being the dependent variable was taken on the x-axis while the square of the
time period on the y-axis. The gradient of the graph equaled
4𝜋 2
𝑔
. After the graph was plotted,
there where few scattering of the coordinates due to the experimental errors hence this line of
best fit was drawn as seen on figure 2. A straight line clearly shows that the relationship
between the length (L). And the square of time is directly proportional. Using this graph, we
calculated the gravitational acceleration as 10.0. This clearly demonstrates that the mass of the
pendulum does not influence the acceleration of the pendulum. Though the experiment was
done to keep the errors minimum, there were still some systematic and random errors in the
experiment. The time for the oscillation was recorded via a mechanical stopwatch, using a
mechanical stopwatch resulted in zero errors as well as parallax errors timing. Human reaction
error could have also contributed to the deflection of the readings. These errors could have
been avoided by using a light gate. The experiments should have also been performed with a
smooth surfaced bulb to make it more aerodynamic and the pivot should have been smoother
to reduce the friction. Also, to note that the uneven air conditioning in the laboratory due to
open windows may have also resulted in some false readings.
6.0 Conclusion:
The experiment successfully fulfilled its purpose. After the experiment, it was shown that the
period of oscillation for a pendulum is independent of mass. Also, it was shown that the mass of
the bob has no effect on the acceleration of the pendulum.
7.0 References:
➢ R.C. Hibbeler (2007). Engineering Mechanics. 11th Edition. Singapore.Pearson Education
➢ John Allan. (2003) The Simple Pendulum.
Answers to the questions on the simple pendulum:
1. The period of a simple pendulum would be longer on the moon than on Earth because
the gravitational force on the moon is weaker than on Earth.
2. If the pendulum rod increases in length with an increase in temperature, the time kept
by a pendulum clock would be longer when the temperature is higher.
3. If the period T were graphed as a function of the square root of the length, the graph
would be a straight line.
4. The mass of the ball does not affect the period of a simple pendulum. Replacing the
steel ball with a wooden ball, a lead ball, or a ping pong ball of the same size would not
change the period of the pendulum.
```