Pulsating Fountains

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Pulsating Fountains
Eugene Baibourin Johnny Davis Luis Miguel
Palomino

• Becky Harrison
• Kelly Motichka
• Elissa Pitts
• Steve Sayers

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The Fountain
3
Objectives

• 1) Film the motion of a pulsating fountain
• 2) Record the height of each movement of the
  fountain in relation to time
• 3) Graph the height of the fountain as a function
  of time
• 4) Look at the video and graphs for patterns

4
DATA COLLECTED

• This graph shows all the data we collected from
  the fountain.
• It compares the 2,008 frames with their height in
  inches.
• Data was collected from 30 frames per second

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We tried a lot of different graphs
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• This graph displays the height of the fountain at
  time t versus the height of the fountain at time
  t 1
• This graph displays the differences between
  consecutive heights

7
Frequency table

• Bins All the possible increments from
  sequential height data (x100). For example a
  height of 4.25 in. followed by a height of 5.00
  in. (rounded to the nearest quarter inch) is 0.75
  inches. Multiply by 100, and we have the data
  value 75.

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Frequency table

• The frequency was found using Microsoft excel
  program, specifically the array command
  FREQUENCY(F2F2009, H2H10), which goes through
  all the data F2-F2009, and compares them to all
  the possible outcomes (bins), and creates a
  frequency distribution.

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Histogram

• The resulting frequency distribution had a
  naturally occurring Gaussian distribution. We
  decided to test the conjecture that the data is
  Gaussian using the chi-square goodness of fit
  test.

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The null hypothesis is that the data is normally
distributed. Since 15.42 lt 16.9 with df9, we
fail to reject the null hypothesis. We now feel
confident about using the normal probability
distribution in our program to create an
artificial water fountain.
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Calculator Program
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Creating the Program

• We designed a calculator program on a TI 84
  computer emulator for mimicking the behavior of
  the fountains.
• We used the percentages from our frequency table
  and a random number generator to choose the
  change in height at each successive step.
• The program asks the user for a starting height
  and then simulates the fountain.

13
Major Flaw

• When this program was tested, a major flaw was
  found. The graph had a tendency of going either
  very high or very low, such as up to 10 (our
  fountain barely went past 5 inches) or to
  negative numbers. This is because this program
  has no provision for a preventing a very low
  probability event from happening multiple times
  in a row.
• In an improved version of this program, the
  probability of successive events would have to be
  calculated and then numerous IF statements would
  have to be written for every possible step. The
  program would proceed in complexity as the number
  of successive events was increased.