PHYSICS EXPERIMENT REPORT (IV)

Basic Physics
“Ayunan Matematis”

Arranged by:
Name : Widya Fransiska Rompas
NIM : 19101105017
Department : Pharmacy
Group : V (Five)

ASSISTANT PROFESSOR

PHYSICS LABORATORY
FACULTY OF MATHEMATICS AND NATURAL SCIENCE
SAM RATULANGI UNIVERSITY
MANADO
2019
A. Aim
1. Determine the acceleration of gravity in the Unsrat.
2. Understand the relationship between harmonic vibrations and acceleration of gravity.
3. Determine the maximum swing speed.
4. Students can apply and interpret into the graph.
B. Equipment Required
- Scale rule
- rope
- ball
- Stative
- Digital counter or stop watch
- arc
C. Introduction
A simple pendulum may be described ideally as a point mass suspended by a massless string from some
point about which it is allowed to swing back and forth in a place. A simple pendulum can be approximated
by a small metal sphere which has a small radius and a large mass when compared relatively to the length and
mass of the light string from which it is suspended. If a pendulum is set in motion so that is swings back and
forth, its motion will be periodic. The time that it takes to make one complete oscillation is defined as the
period T. Another useful quantity used to describe periodic motion is the frequency of oscillation. The
frequency f of the oscillations is the number of oscillations that occur per unit time and is the inverse of the
period, f = 1/T
( Cutnell, 2013)
Similarly, the period is the inverse of the frequency, T = l/f. The maximum distance that the mass is
displaced from its equilibrium position is defined as the amplitude of the oscillation.
When a simple pendulum is displaced from its equilibrium position, there will be a restoring force that moves
the pendulum back towards its equilibrium position. As the motion of the pendulum carries it past the
equilibrium position, the restoring force changes its direction so that it is still directed towards the equilibrium
position. If the restoring force F G is opposite and directly proportional to the displacement x from the
equilibrium position, so that it satisfies the relationship

then the motion of the pendulum will be simple harmonic motion and its period can be calculated using the
equation for the period of simple harmonic motion
 The mathematical pendulum is a mathematical one that moves following simple harmonic motion.
mathematical pendulum is an ideal object consisting of a point of mass suspended from a lightweight rope with
no mass. if the pendulum is distorted with an angle θ from its equilibrium position then released, the pendulum
will swing in the vertical plane due to the influence of the gravity force. "Based on the decline in Newton's
laws mentioned that the period of simple pendulum swing can be calculated as follows, T = 2π √ (l / g) Where
T: Swing period (seconds). l: Length of the rope (m). (Arief, 2015 ).
In the mathematical swing experiment, we use a swing made in such a way that the load is a physical pendulum.
The basis of experiments using pendulum can not be separated from vibration where the notion of vibration is
a periodic alternating movement through the equilibrium point. Vibration can be both simple and complex.
The vibration discussed about the pendulum is a simple harmonic vibration that is a vibration where the
resultant force acting at an arbitrary point always leads to an equilibrium point and the resultant force is
proportional to the distance of any arbitrary point.
Mathematical pendulum is the point of an object that is hung on a fixed point with a rope. If the swing of the
object deviates at an angle q to the vertical line then the force returning is:
F = - m . g . sin q
For q in the radial that is q small then sin q = q = s / l, where s = the arc of the ball and l = the length of the
rope, so that:

If there are no friction and twisting forces then the equation of force is:

or
This is the differential equation of vibration in harmony with the period is:

With a mathematical pendulum then the acceleration due to gravity g can be determined ie by relationship:

The prices of l and T can be measured in the conduct of experiments with metal balls that are heavy
enough to be hung with very light wires (Anonymous, 2007).
Motion oscillation that is often found is the swing motion. If the oscillation deviation is not too large, then the
motion occurs in simple harmonic motion. A simple swing is a system that consists of a mass and cannot
stretch. This is shown in the picture below. If the swing is pulled sideways from the equilibrium position, and
then released, the mass m will swing in the vertical plane under the influence of gravity. This motion is
oscillatory and periodic motion. We want to determine the swing period. In the picture below, a swing of length
1, with a particle of mass m, is shown, which creates an angle θ to the vertical direction. The force acting on a

particle is the gravity and tensile force in a rope. We choose a coordinate system with one axis tangent
to the circle of motion (tangential) and another axis in the radial direction. Then we describe the gravity for the
components in the radial direction, i.e. mg cos θ, and tangential direction, ie mg sin θ.
The radial component of the forces at work provides the centripetal acceleration needed for the object to move
in an arc. The tangential component is the inverting force on the body m which tends to return the equilibrium
to the mass of equilibrium. So the inverting force is:

(Giancoli, Douglas.1998)
The oscillation motion we often encounter is swing motion. This oscillation motion takes place under
the influence of Earth's gravitational force. If the swing deviation is not too large, then the shape of the
oscillations is simple harmonic motion. This simple harmonic motion occurs because there is a style
(heaviness) that occurs in objects whose direction is always directional to the center of the equilibrium point.
Great reverse style expressed in Hooke's law as with K is the setting.
If a mass point is hung (by a mass rope) at the O Point, and the mass is rounded up so as to form the
angle against the vertical axis in the O point. After the removable m will move towards its
steering point by the F-back style which is a component of the heavy force on M. If the length of the strap is
L, and the Earth's gravity acceleration g then F can be written as:

If the trajectory is small so that the crossbow ball (S) is also small, then

and backstroke can be written as:

For the swing is as simple as vibration aligned then there is no (if there can be ignored) the air friction style
and the style of the twisting on the rope so that the resultional style equation is:

The equation is a simple aligned vibration equation and S is a periodic function with the period T that fulfills
the equation:
 Figure 6.1. Style Diagram on mathematical penal experiments
(Verna, 2019)
Examples of mechanical swing categories are the pendulum.
The recovery force arises as a consequence of gravity on the M mass ball in the form of the Mg gravitational
force which negates each other with the Mdv / dt force related to inertia. The swing frequency does not depend
on the mass of M.
In the case of the swing system as presented in the picture above, the mass movement M is limited or
determined by the length of the pendulum L, and the applicable equation of motion is:

where in this case the speed of the ball along its path in the form of a circular arc is. The sinθ factor is the
component in the direction of gravity of the force acting on the ball in the θ direction. Next, by removing M

from both sides of the equation above, a shape is obtained , which is a nonlinear differential
equation for θ.
If it is considered the initial deviation of the swing is quite small, then it applies sin θ = θ so that the equation
can be transformed into a linear form as follows,

The equation is an illustration for a sinusoidal swing with a frequency given by:

maka
(Sutrisno, 1979)
D. Procedur
1. Arrange the experiment tool as shown

2. Set the length of the rope to the base of the ball is 120 cm, 110 cm, 100 cm, .., or according to the
instructions of the lecturer / assistant.
3. Round the swing so that it forms an angle of about 5° to 10°, then release.
4. Measure the time for 15 swings for each length of rope.
5. Perform 3 repetitions for each length of the rope.

E. Result
( Terlampir )
F. Analysis
Pada praktikum ini, praktikan melakukan sepuluh kali percobaan, yang dalam setiap percobaan
dilakukan tiga kali pengulangan untuk tiap-tiap ukuram tali. Ayunan bergeraak secara harmonik dan
dihitung sebanyak lima belas kali untuk setiap tali yang panjang berbeda yaitu 120 cm, 110 cm, 100 cm,
90 cm, 80 cm, 70 cm, 60 cm, 50 cm, 40 cm, 30 cm.
Dengan beban matematis ini, percepatan gravitasi (g) dapat ditentukan setelah diketahui berapa
besarnya periode dimana periode berbanding terbalik dengan gravitasi (g). Pada percobaan ini beban akan
berayun –ayun apabila tali dimiringkan dengan sudut 100. Hal ini disebabkan kareana adanya gaya yang
besarnya sebanding dengan jarak dari suatu titik, sehingga selalu menuju titik kesetimbangan. Benda
melakukan getaran secara lengkap apabila benda mulai bergerak dari titik dimana benda tersebut
dilepaskan.
Pada praktikum ayunan matematis ini alat harus siap pakai terutama stopwatch karena pada saat ayunan
dihentikan stopwatch juga harus bersaan berhenti. Penggunaaan panjang tali juga mempengaruhi untuk
waktu yang diperlukan terhadap 15 kali ayunan.
Berdasarkan hasil yang telah dilakukan dalam percobaan ini, diketahui bahwa semakin pendek tali yang
digunakan, maka waktu untuk 15 kali ayunan semakin kecil.
Bahwa pengaruh panjang tali sangat menentukan banyak getaran yang dihasilkan oleh bandul. Semakin
panjang tali maka semakin kecil getaran dan frekuensi yang dihasilkan, sedangkan periodenya semakin
bertambah. Hal ini dikarenakan jika tali semakin panjang, maka akan sulit untuk bandul berayun sehingga
bandul akan bergerak semakin lambat.
Kendala-kendala yang praktikan alami yaitu kurang teliti saat mengukur derajat yang mulai tinggi
menyebabkan sangat susah untuk dijangkau, karena sangat tinggi dan peralatan yang digunakan sangat
sedeerhana. Pada saat pengukuran sudut ada kemungkinan pengukurannya berlebih dan mungkin juga
kurang.
Hal yang menyebabkan pengukurannya tidak sama yaitu faktor kurang ketelitian saat menghitung
waktu dan mengukur sudut, saat mengukur di ketinggian yang tinggi sehingga menyebabkan data yang
diperoleh tidak sama, bahkan ada yang selisihnya sangat jauh.
Dalam praktikkum dibuktikan bahwa tali memengaruhi kecepatan dalam pergerakan bandul. Semakin
pendek tali yang digunakan, maka semakin cepat pergerakan bandul dalam gerakan harmonic sederhana.
Sebaliknya, semakin panjang tali, maka bandul akan bergerak lebih lama. Tetapi, semakin pendek tali,
ditemukan bahwa gravitasi yang didapatkan bahkan tidak sampai 9,8 m/s2. Sehingga semakin pendek tali,
gravitasi pun ditemukan makin kecil. Perhitungan gravitasi yang tidak mencapai tetapan 9,8 m/s memilki
beberapa hal yang berpengaruh, seperti ketinggian, faktor ayunan, tempat, benturan, kesalahan praktikkan
dan hal-hal lainnya.
G. Conclusion
1. Dalam perhitungan, gravitasi di unsrat adalah 9,655 m/s2 berdasarkan percobaan pertama dalam
ayunan matematis.
2. Gerak harmonic sederhana terjadi di bawah pengaruh gaya gravitasi bumi. Tanpa adanya gravitasi
bumi, gerak harmonic sederhana, tidak akan bergerak secara harmonic dan berulang berulang.
3. Kecapatan maksimal setiap ayunan berbeda-beda dan ditentukan berdasarkan kecepatan bandul dan
selisih ketinggian bandul bergerak.
4. Data yang ada dapat diinterpretasikan ke dalam bentuk grafik, denngan mengambil data antara
panjang tali, dan periode pangkat 2
Reference
Anonim.2007.Ensiklopedia Ilmu Pengetahuan Alam (Fisika).Semarang:Aneka Ilmu
Cutnell, dkk.2013.Introduction to PHYSICS.John Wiley & Sons Singapore Pte,Ltd.
Giancoli, Douglas.1998. PHYSICS Fifth Edition. Pretince-Hall, Inc.
Hidyat, Arief. Ayunan Matematis. Dari jurnal :
https://www.academia.edu/people/search?utf8=%E2%9C%93&q=ayunan+matematis
Sutrisno.1979.Fisika Dasar.ITB.Bandung.
Verna,S.,dkk.2019.Modul Praktikum FISIKA DASAR,Unsra