Stella

STELLA version 10:

Pendulum Story

Muhammad Riyadh b RoslanUniversity of Education Sultan Idris.

Introduction

I use the software STELLA® from isee systems (http://www.iseesystems.com/) to model

a pendulum. Pendulum is usually very complex, having many components with

involved relationships. For example, we can use STELLA to model the pendulum having

the relationship between the mass, the displacement and the length f the string.

The pendulum is a body suspended from a fixed point so as to swing freely to and

fro under the action of gravity. Its regular motion has served as the basis for

measurement, as recognized by Galileo. Huygens applied the principle to clock

mechanisms. The pendulum serves as an illustration of Newton’s Second Law, which

states that for every force there is an equal and opposite reaction. The simpler

experiments illustrate another of Newton’s laws, namely, that a body in motion continues

in motion unless acted upon by another force. The pendulum offers an extensive array of

experiments that can be done using easy to obtain, inexpensive materials. The

measurements require no special skills and equipment. The graphical results of each

experiment are given, and can be compared to the results calculated from a simple

equation if desired. Without doing the real experiment, we can use a simulation that is

called STELLA to represent the experiment.

Simulation

STELLA v10 Pendulum story. 2

What is simulation? As you know, simulation of a system is the operation of a

model, which is a representation of that system. While a model is representation of an

object, a system, or an idea in some form other than that of the entity itself. Model can be

categorized by two types of models, which is the physical model (Scale model, prototype

plants, etc.) and mathematical model (Analytical queuing models, linear programs,

simulation. etc.). In this sample, a model is the Pendulum story, while the simulation is

the STELLA. The model is amenable to manipulation which would be impossible, too

expensive, or too impractical to perform on the system which it portrays. The operation

of the model can be studied, and, from this, properties concerning the behavior of the

actual system can be inferred.

The simulation system has many applications, such as:

Designing and analyzing manufacturing systems

Evaluating H/W and S/W requirements for a computer system.

Evaluating a new military weapons systems or tactics

Determining ordering policies for an inventory system

Designing communications systems and message protocols for them.

Designing and operating transportation facilities such as freeways, airports,

subways, or ports.

Evaluating designs for service, organizations such as hospitals, post offices, or fast

food restaurants.

Analyzing financial or economical systems.

Why should we teach the students by using simulation? we should teach the students by

using simulation because it creates a deep learning between the students. The students

will get a good summary of what they learn by using simulation then by using a real life

experiment Other than that, the students will develop a feel for what variables are

important and the significance of magnitude changes in parameters

Contents


Pic1: the beginning of the simulation.

This is the front simulation page of STELLA’s sample (pendulum story). It is a

learning laboratory created with STELLA. It contains background, conduct experiment

and explore the model. The sample is created by the Isee System to give the user an

overview about what is STELLA all about. As you can see, STELLA has copyright this

sample in 2012. First, I will go to the background of this sample.


Pic2: Background and Context

“Consider what happens when you connect a small ball (or bob) to the end of a

string. When the bob is pulled a short distance away from its rest position and released, it

will begin to swing back and forth. This system is called a simple pendulum and the type

of motion is called simple harmonic motion.

In this system it is assumed that the mass of the bob is concentrated at a point and that

the mass of the string is negligible.

In this model, you will explore the effect that string length, bob mass, and initial starting

position have on the motion of the pendulum, ignoring the effects of friction and air

resistance. Then, you will investigate how the motion is changed when other forces are

taken into account.”


The background and context is about what is the purpose of this experiment. It tells

us what the benefits of using this simulator are. Ignoring the friction and air resistance,

we can get an accurate reading of the experiment. After reading the background and

context of the sample, I go forward to the next content which is conduct the experiment.

Pic3 : Conduct Experiments (Pendulum Story)

This interface simulation of the experiment that simulate a pendulum experiment

onto a computerized program that will provide an accurate reading without any error that

we usually encountered during a real life experiment. The set of data that can be

manipulated are mass of ball (kg), initial displacement (m), and string length (m). While

gravity only, add friction and add driving force button is a simulated external error that

usually we can encounter easily during real life experiment. We can only choose one of

the simulated external error button by click either one of the button that we want to

include in the experiment.


Pic4: Experiment run without changing any value.

After running the experiment without changing any value to the simulation, we get

a graph shown as above. The pendulum oscillates at a displacement of 0.1m from its

origin. The length of the string that is use is about 0.1m with a weight of 1kg. This graph

tells us that the period of 1kg ball with a initial displacement 0.1m at a length of 0.1m

oscillates at a period of 2 seconds for every 1 complete oscillation. The oscillations of the

pendulum create a sinusoidal graph due to it’s forth and back oscillation. The simulation

Run – To start the experiment by showing the flow of the graph.

Pause – to temporarily stop the experiment by pause the flow of the graph.

Stop – Stop the experiment.

Reset – restart the experiment to its default state.


creates a simulated oscillation without damping. In real life, the experiment is conducted

in vacuum condition.

Pic5: Experiment run by changing the value of the mass to 2.00kg

After changing the value of the mass of the ball to 2.00, the graph shows no change

from the previous graph. The period of the oscillation still at the same pace. This shows

us that, the period of the oscillations does not depend on the mass of the ball. Either the

ball is heavier or lighter, the period of the heavier ball still progress at the same pace with

the lighter ball. This concept is same as the concept of free fall whereby an object with

different weight is drop at same altitude will reach the ground at the same time.


Pic6: Experiment run by changing the value of the initial displacement.

After adjusting the initial displacement, the graph still has the same sinusoidal

shape, but at the start of the graph has change for 0.10m of displacement to 0.20m of

displacement at a period 0 second. This shows us that the initial displacement of the

pendulum only increase the amplitude of the sinusoidal graph. It does not affect the

period of the oscillation because it still oscillates at a period of 2 seconds for every 1

complete oscillations. It does not affect the period because the kinetic energy and the

potential energy have been balanced when the pendulum oscillates. When the pendulum

is at the highest position, the kinetic energy is equal to 0J, while the potential energy will

be at the maximum possible value. While, when the pendulum is at the origin, the

condition become vice versa as the potential energy will be equal to 0J and the kinetic

will be at the maximum possible value according to its velocity and mass.


Pic7: Experiment run by changing the value of the string length.

After changing the value of the string length, we get the graph as shown above. The

sinusoidal graph is a bit different from the previous graph as it frequency has altered. The

period of the graph has increased from 2 seconds to 2.8 seconds. This happen because the

length of the string has been increased to 2.0m, thus increases the oscillations period. We

can say that the longer the string length, the longer the time taken for the oscillation to

complete its one complete oscillations. To get a shorter period of time, we just need to

shorten the length of the string.

From the previous graph, we have known that only the string length can affect the

period of the pendulum’s oscillation when we apply only gravity acted on it. But, what

happen when we add friction or add driving force that acted upon the pendulum

oscillations? Does anything happen to the graph? Can it affect the period of the

oscillation? The questions can be answer by using this simulated pendulum experiment

only by clicking the “add friction” button and “add driving force” button.


Pic8: Experiment run by adding friction upon the experiment.

After clicking the button “add friction”, the sinusoidal graph does not appear to

have a similarity with the previous graph. The graph’s amplitude starting to decreases for

every 1 second interval. In other word, the process is called as damping. It happens when

the ball bearing of the pendulum had a contact with air friction, thus reducing the

velocity of the pendulum. More energy is lost when there is an air friction between the

ball and the air. In order to increase the air friction of the pendulum, we can increase the

surface area of the ball.


Pic9: Experiment run by adding driving force to the experiment.

This experiment was run by adding driving force, but because of the driving force

graph shows same similarity with the pic1, I have decided to compare and combine the

graph from the pic1. The red line graph represents pic1 which is the default state, while

the blue line graph represents the “add driving force” graph. Between these two graphs, it

is almost looks like both of them overlap; but actually, the blue line graph’s amplitude is

lower that the red line amplitude.

As a conclusion, STELLA is a great tool for us to teach the children nowadays to

understanding the objectives of their lessons. Moreover, STELLA can greatly reduce our

expenses to recreate a laboratory experiment. It cut the cost to buy the apparatus needed

to accomplish the experiments objective. Other than that, STELLA is more accurate than

a real life experiment. It also provide efficiency in creating the graph. Without doing a

lot of work, STELLA help us reduce the labor work, by helping us create an accurate

graph base on equation and simulation. Overall, STELLA is a new way of educating the

21st century students.

Stella

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