Simulations can be
considered a variant of cognitive tools, for example they allow students to
test hypothesis and more generally "what-if" scenarios. In addition,
they can enable learners to ground cognitive understanding of their action in a
situation. Simulation is a powerful tool for analyzing, designing, and
operating complex systems. It enables you to test hypotheses without having to
carry them out, saving you thousands, even hundreds of thousands of dollars. It
is a cost-effective means of exploring new processes, without having to resort
to pilot programs. Simulation provides a method for checking your understanding
of the world around you and helps you produce better results faster. And it is
an efficient communication tool, showing how an operation works while
stimulating creative thinking about how it can be improved. Simulation is used
in many contexts, such as simulation of technology for performance
optimization, safety engineering, testing, training, education, and video
games. Training simulators include flight simulators for training aircraft
pilots to provide them with a lifelike experience. Simulation is also used with
scientific modelling of natural systems or human systems to gain insight into
their functioning. Simulation can be used to show the eventual real effects of
alternative conditions and courses of action. Simulation is also used when the
real system cannot be engaged, because it may not be accessible, or it may be
dangerous or unacceptable to engage, or it is being designed but not yet built,
or it may simply not exist. Simulation is extensively used for educational
purposes. It is frequently used by way of adaptive hypermedia. Simulation is
often used in the training of civilian and military personnel. This usually
occurs when it is prohibitively expensive or simply too dangerous to allow
trainees to use the real equipment in the real world. In such situations they
will spend time learning valuable lessons in a "safe" virtual
environment yet living a lifelike experience (or at least it is the goal).
Often the convenience is to permit mistakes during training for a
safety-critical system. For example in Smart School, teachers practice
classroom management and teaching techniques on simulated students, which
avoids "learning on the job" that can damage real students. Simulation
can integrate into teaching and learning because Simulations support learning
by allowing a pupil to explore phenomena and handle experiments which would not
be feasible in school. Teachers can also
focusing attention on underlying concepts and relationships. Simulations offer
idealised representations that limit the range of operating variables to good
effect.
Modelling is about
building representations of things in the ‘real world’ and allowing ideas to be
investigated. It is central to all activities in the process for building or
creating an artifact of some form or other. In effect, a model is a way of
expressing a particular view of an identifiable system of some kind. Models
are, in one respect, idealizations in the sense that they are less complicated
than reality, they are simplifications of reality. The benefit arises from the
fact that only the properties of the world relevant to the job in hand are
represented. For example, a road map is a model of a particular part of the
earth's surface. We do not show things like vegetation or birds' nests as they
are not relevant to the map's purpose. We use a road map to plan our journeys
from one place to another and so the map should only contain those aspects of
the real world that serve the purpose of planning journeys. One of the
simulator software is the STELLA software. STELLA offers a practical way to
dynamically visualize and communicate how complex systems and ideas really
work. STELLA models enable us to communicate how a system works like what goes
in, how the system is impacted, what are the outcomes.
STELLA supports diverse
learning styles with a wide range of storytelling features. Diagrams, charts,
and animation help visual learners discover relationships between variables in
an equation. Verbal learners might surround visual models with words or attach
documents to explain the impact of a new environmental policy.
The purposes of STELLA
usage are to stimulate a system over time, jump the gap between theory and the
real world, enable students to creatively change systems, teach students to
look for relationships and clearly communicate system inputs and outputs and
demonstrate outcome.
The example of the
sample model that can be found in the STELLA website is pendulum story. A
simple pendulum is one which can be considered to be a point mass suspended
from a string or rod of negligible mass. It is a resonant system with a single
resonant frequency. A simple pendulum consists of an object suspended by a
string of length l. The bob swings back and force. The gravitational force, the
weight (W), is resolved into two components. The parallel component is along
the direction of the spring. The perpendicular component is at right angles to
the direction of the spring. When the bob is pulled to the right, the
perpendicular component is to the left, and vice versa. That is, the component
of the weight (perpendicular), is a restoring force. Further, for small angles
(less than 15°) the magnitude of perpendicular component is proportional to the
displacement of the bob. Thus, small-displacement pendulum motion is an example
of simple harmonic motion. The time for one complete cycle, a left swing and a
right swing, is called the period. A pendulum swings with a specific period
which depends (mainly) on its length. When given an initial push, it will swing
back and forth at constant amplitude. Real pendulums are subject to friction
and air drag, so the amplitude of their swings declines. The period of swing of
a simple gravity pendulum depends on its length, the local strength of gravity,
and to a small extent on the maximum angle that the pendulum swings away from
vertical, θ0, called the amplitude. It is independent of the mass of the bob.
If the amplitude is limited to small swings, the period T of a simple pendulum,
the time taken for a complete cycle. For small swings the period of swing is
approximately the same for different size swings: that is, the period is
independent of amplitude. Successive swings of the pendulum, even if changing
in amplitude, take the same amount of time. For larger amplitudes, the period
increases gradually with amplitude.
There are three
different types of oscillation that are free oscillation, damped oscillation and
fixed oscillation. Free oscillations occur while the pendulum is sets to its
displacement and is moving in its to and fro motion it does not experience any
force that prevents it from continuing this motion. Such forces that prevent
free oscillation is air resistance. Damped oscillations occur while the
pendulum is set to its displacement and is moving in it to and fro motion,
experiences a force, or a medium that affects its motion. A forced oscillation
occurs while an object is used to force or more pendulums into motion. An
example of this is by using a driving pendulum to control the displacement of a
set of 4 pendulums, which move as a result of the driving pendulum being
displaced. Other than that, the other example is using a vibrating tuning fork
to force a stretched string to vibrate and set the pendulum into motion. The
simple gravity pendulum is an idealized mathematical model of a pendulum. This
is a weight or bob on the end of a massless cord suspended from a pivot,
without friction. When given an initial push, it will swing back and forth at constant
amplitude. Real pendulums are subject to friction and air drag, so the
amplitude of their swings declines.
Picture 1: the front page of the pendulum sample in STELLA
This software is a
shareware type of software. So, we need the license to use this software. As
the trial, we are given free trial version that will time out 30 days after the
installation. We need to register at the website to download the software. The
picture above is the free trial version of STELLA. By using STELLA software,
the student can relate the result of the simulation to the theorem of simple
pendulum. This is because the can varied the variable that affect the
experiment such as mass of the bob, string length, initial displacement, air
friction and driving force. In the task given by Encik Azmi to us, we need to find
discuss about three variables that affect the experiment we choose to use in
the STELLA software. By using the STELLA software, my variables are string
length, initial displacement and mass of the bob.
Picture 2: the oscillation of the pendulum at the normal
condition
At the STELLA software,
we click the button “conduct experiments” to begin the experiment of the simple
pendulum. From picture 2, I choose the normal condition to be a guideline to
compare with latter experiments. As the guideline, I fixed the mass of the ball
is 1.0 kg, initial displacement is 0.1 m, and the string length at 1m. By put
the normal condition oscillation together with the graph that I change the
parameter, I can compare directly to make the analysis of the experiment. All
the experiment that I done is only under the gravitational force and not
include the air friction and drive force.
Picture 3: change of mass of bob
The first parameter I
change is the mass of pendulum. From
picture 3 above, graph 1 is the oscillation at normal condition (mass=1kg,
initial displacement=0.1m and string length=1.0m), graph 2 at the mass of
pendulum is half the initial mass of pendulum of normal condition (mass=0.5kg,
initial displacement=0.1m and string length=1.0m) and graph 3 is the pendulum
with double mass of the pendulum at normal condition (mass=2.0kg, initial
displacement=0.1m and string length=1.0m). So, from the graph, we see that all
the graph have the same frequency, amplitude and period. This situation shows
that the mass does not affect the oscillation of pendulum. To find the period
of oscillation of the pendulum, we use
And we found that the
mass not one of the parameter that change the period of oscillation. So, the
graph in picture 3 proves the equation
Picture 4: changes of initial displacement of bob
. From the picture 4, I
simulate the oscillation at different initial displacements. Graph 1 is at
normal condition that will become the guideline of other graph, graph 2 is the
pendulum with initial displacement of 0.15m and graph 3 with initial displacement
of 0.2m. From the graph, we can see that the frequency of all graphs is same
with each other and different with the amplitude of the graph. When the initial
displacement increase, the height of displacement also increases, the potential
energy increases, so kinetic energy also increase but the time period remains
same.
Picture 5: changes in length of string
Next, the parameter
change is the length of string of the pendulum. From the picture 3, we have the
graphs. Graph 1 is the oscillation at the normal condition (mass=1kg, initial
length=0.1m and length of string=1.0m), graph 2 with the length of string is
half than the length of string at normal condition (mass=1kg, initial
length=0.1m and length of string=0.5m) and graph 3 at the condition where the
length of string is double the normal length of string of pendulum (mass=1kg,
initial length=0.1m and length of string=2.0m). From the picture 3, the
amplitude of all graphs is same but different with the period of oscillation.
The period of oscillation is increase directly with increasing the length of
the string of pendulum. From the equation period of oscillation that I stated
above, length of string a factor that changes the oscillation of pendulum. The
obtained graphs prove that equation. As a conclusion from the experiment,
there are two factors that affect the period, frequency and amplitude of the
pendulum. In this case, initial and length of the string affect the period of
oscillation, frequency and amplitude of the pendulum while the other parameter
that is mass of the ball do not affect the motion of the pendulum.
By using STELLA software
to conduct the experiment, we can see that the data obtained is very accurate.
For example, if we conduct the experiment of pendulum with different masses manually,
we barely get the expected data and graph like picture 2.
