Part 1: Calculations
There may be many things going on around you that are periodic that you do not even realize!
Perhaps there is an old grandfather clock in your house, with a pendulum swinging back and forth inside. That
pendulum is one example of periodic motion that can be graphed using trigonometric functions. How about the hands on the face of that same grandfather clock? They repeat the same pattern every 12 hours, 60 minutes, and 60 seconds. The tides rise and fall in a periodic fashion, the planets travel around the sun, and the earth rotates on its axis. These are all examples of periodic motion! Your assignment is to choose an object, or event, around you that can be represented by trigonometric functions, then complete the following tasks.Record your event through a series of photographs, a video or another appropriate method. (For example,
if you are using an oscilloscope, include a photo or video of the sound wave, and a copy of the audio file
that you are measuring; If you are using a website like this one: http://astro.unl.edu/, include a
screenshot, or create a video using Jing).
2) Record the starting yvalue of your object or event (when x = 0).
3) Find the period of the object or event.
4)
Find the maximum and minimum yvalues. You will need to pick a base point to reference from (usually
this is a stationary object that you can measure from. For example, a stationary dock if measuring the
tides).
5) Determine the amplitude of the function.6) Determine the vertical translation of the function.
7) Use the information gathered to create a function of the form f(x) = a sin(k(x-d))+c , and a function of the form f(x) = a cos (k(x-d)) + c.
Graph your functions by hand. (Remember to include appropriate labels, scale, etc.)
Using the functions that you have created, determine the y value at the point x = period/3 and x = (5/6)*period
(For example, if your period is 4 , then4π/3 ) Part 2: Presentation and Reflection
At this point in the course, you have submitted several assignments of various types. For this assignment, you may choose how you would like to present your findings. Please remember that your submission should be appropriate to the course, should be clear and easy to follow, neat and organized. See the rubric for this assignment for further details.1) Describe in your own words why the object or event you chose is periodic.
2) Explain your process for coming up with the functions that represent your object or event. Explain the
point of reference you chose and why you chose it, how you measured or gathered the data you need, etc.
3) Explain a method you could use to verify that your functions are accurate (think about ways you have
verified functions before, this may have been done in other units, or other courses).
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Real-World Periodic Functions - Virtual High School (VHS) - MHF4U
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Unit Assignment: Real - World Periodic Functions
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Part 1: Calculations
There may be many things going on around you that are periodic that you do not
even realize!
Perhaps there is an old grandfather clock in your house, with a pendulum swinging
back and forth inside. That pendulum is one example of periodic motion that can be
graphed using trigonometric functions. How about the hands on the face of that
same grandfather clock? They repeat the same pattern every 12 hours, 60 minutes,
and 60 seconds. The tides rise and fall in a periodic fashion, the planets travel
around the sun, and the earth rotates on its axis. These are all examples of periodic
motion!
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Please contact to get complete assignment
Email - admin@panhelp.com
Question 1.
Your assignment is to choose an object, or
event, around you that can be represented by
trigonometric functions, then complete the
following tasks.
1) Record your event through a series of
photographs, a video or another
appropriate method. (For example,
if you are using an oscilloscope, include a
photo or video of the sound wave, and a
copy of the audio file that you are
measuring; If you are using a website like
this one: http://astro.unl.edu/, include a
screenshot, or create a video using Jing).
2) Record the starting y value of your object
or event (when x = 0).
3) Find the period of the object or event.
1.
To illustrate a periodic function in every-day life, I chose to record
the movement of the pendulum on cuckoo-clock for about 5
seconds. The video is attached with the file. Every two ticks
illustrates one second and during one second (approx) the
pendulum moves from the A back to equilibrium and the other
side (G) and then back to equilibrium and A. The value (D)
represents the equilibrium point and the distance between the
pendulum and A and the pendulum and G is approx 3.5 cm each
way.
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4) Find the maximum and minimum y -
value. You will need to pick a base point
to reference from (usually this is a
stationary object that you can measure
from. For example, a stationary dock if
measuring the tides).
5) Determine the amplitude of the
function.
6) Determine the vertical translation of
the function.
7) Use the information gathered to create
a function of the form f(x) = a sin(k(x-
d))+c , and a function of the
form f(x) = a cos (k(x-d)) + c.
8) Graph your functions by hand.
(Remember to include appropriate
labels, scale, etc.)
9) Using the functions that you have
created, determine the y value at the
point x = period/3 and x =
(5/6)*period
(For example, if your period is 4 ,
then4π/3 )
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Part 2: Presentation and Reflection
At this point in the course, you have submitted several assignments of various types.
For this assignment, you may choose how you would like to present your findings.
Please remember that your submission should be appropriate to the course, should
be clear and easy to follow, neat and organized. See the rubric for this assignment
for further details
6. Assignment Help | 100% Plagiarism Free | Success Assured | Email Now to get quote – admin@panhelp.com
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Be sure your submission answers the
following questions as well:
1) Describe in your own words why the
object or event you chose is periodic.
2) Explain your process for coming up with
the functions that represent your object or
event. Explain the
point of reference you chose and why you
chose it, how you measured or gathered the
data you need, etc.
3) Explain a method you could use to verify
that your functions are accurate (think about
ways you have
verified functions before, this may have been
done in other units, or other courses).
4) Reflect on the assignment. What part of
the assignment did you find most difficult?
What did you find the
easiest? What did you learn while working
through this assignment?
Question 2.
