SIMPLE PENDULUM
Construct a pendulum that swings.
Make the motion realistic, and make the period
of the pendulum dependent on its length in a realistic way. (69)
OBJECTIVES
Mathematics:
(Preknowledge: M.6.3.3.3. Çapı veya yarıçapı verilen bir çemberin
uzunluğunu hesaplamayı gerektiren problemleri çözer.)
M.71.4.3 Gerçek yaşam durumlarını, tabloları veya doğru grafiklerini
inceleyerek iki çokluğun orantılı olup olmadığına karar verir.
Physics:
12.2.1.1. Basit harmonik hareketi açıklar ve örnekler verir.
12.2.1.2. Düzgün çembersel ve basit harmonik hareket yapan yay ve sarkaç
hareketleri arasındaki ilişkiyi açıklar.
12.2.1.5. Esnek bir yayla ucuna bağlı bir cisimden oluşan sistemde ve basit
sarkaçta
periyodun bağlı olduğu değişkenleri analiz eder.
12.2.1.6. Basit sarkaç ve esnek bir yayla ucuna bağlı bir cisimden oluşan
sistemin periyodu ile ilgili hesaplamalar yapar.
PEDAGOGICAL EXPLANATION
Our
simulation is a dynamic model to show simple pendulum motion. Basicly, it is
created to show that period of the simple pendulum equation is depends on the
lenght of the rope. Students will see, as the length increase, period of the
pendulum will increase too. Here, students need to know circumference of the
circle as a preknowledge (M.6.3.3.3) and then they will see the proportional
relationship between lenght of the rope and the period. (M.7.4.3). Our main aim
is to show speed and mass are not the variables of the period, but length of
rope affects the circumference of the circle. Therefore, the period is affected
because of the circumference.
This
pendulum model needs to be constructed by students so the teacher take a role
as a guide. Creating/constructing a structure by themselves will help more,
because it is one of the good learning methods. Students will focus on how to
construct an equation with one variable and how different lengths will be
satisfied by the equation.
There
may different kinds of solutions to show this pendulum motion. Our model is one
of them and it is easy to construct so after students apply our construction, they
may add more features on it. They may show the proportional relationship with
another equation or they can add a kronometer to count period.
The
strenght of this model is it is easy to use and to see the motion. There are
only two button so there won’t be a confusion about button usage. On the other
hand, we tried to add a clock to count time while swinging but we could not be
able to add it so it is one of our weaknesses. Also the rope can move as circular
motion perpendicular to the pendulum but it requires to have three dimensional
platform so this is another weakness of our simulation.
USER MANUEL
If you are a teacher and you want
to show this tool on board etc....
You can use this tool while you are
introducing the simple pendulum motion and ask your students what the variables
may be. Also you can ask what they think about speed and mass. After showing
the tool and the equation, you can ask them to draw the motion and relate it
with the circle. “What is the relationship between lenght of this rope and the
time of one oscillation? Why it is just depends on the length of the rope? Can
you show the proportional relatinship by showing the circumference of the
circle?” These may further questions to be asked.
If you are a student and the model
is asked you to be constructed....
1)
Please
open the Geometer’s Sketchpad Program and begin with a parameter which is
length of the rope. Other parameter will be gravity.
2)
Constructing
a circle by radius (lenght parameter) and center point. Please add a segment from
center (Point A) to (Point B) on the circle.
3)
Put
on point A on your segment and again construct your second circle by center
(point A) to point B. Now your second circle will move as Point B moves.
4)
Construct
an arc thorugh 3 points which includes Point A.
5)
We
need a segment which can move therefore you need to construct a second segment
from Point C to your arc.
6)
Now
I want you to create two movement(animation). One of them should be for the
second segment, it will swing on the arc. Second one is for the second
circle which needs to be shrink while the rope swings. Please figure out how to
create these two movements.
7)
After
you create these two animation, add two more reset buttons to make your model
go to the beginning.
8)
Represent these two animations as a pendulum button and also represent other two reset buttons on a
one reset button.
9)
Now
write your period equation from the calculate section.
10) Please hide buttons and
construction tools as much as you can. Just left necessary parts.
Video link : https://www.youtube.com/watch?v=vWxPmH7gzMQ
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