Finding the Mathematical Model of a Sinusoid

1
Finding the Mathematical Model of a Sinusoid
Y K A sin(D(X-H))
Using SNDDEMO data recorded as volts vs time.
2
Step 1
Find a local maximum and minimum point near the
start of the data using the TRACE function.
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Step 2
Find a local maximum and minimum point near the
end of the data. Record the values.
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Step 3
Find the vertical shift (k) value.
The vertical shift is the midline of the data
set. It can be approximated by averaging the
local maximum and minimum values.
The midline value (k) is 2.6993 volts.
Graphing the midline value (y 2.70) on the
current data set.
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Step 4
Find the amplitude (a) value.
The amplitude is the maximal change in the data
from the midline.
To find the amplitudeSubtract the midline from
the local maximum value.
The amplitude is 0.016 volts.
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Step 5
Find the period and frequency.

• Find two local max/min values.

• Find the difference of the x-coordinates.
  (.2025 - .06) .1425 sec

• Count the number of cycles from the starting to
  ending point. 2 cycles

• Divide the difference by the number of cycles
  to determine the period. 0.07125
  seconds/cycle or a period of 0.07125

• Find the reciprocal of the period for the
  frequency. 14.04 cps

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Step 6
Find the horizontal stretch/shrink (d) value.
The d value in the model is the number of times
the period repeats in 2? radians.
The horizontal stretch/shrink (d) value is
88.1851 radians / second.
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Step 7
Find the horizontal shift (h) value.
A period of sine begins when the graph crossing
the midline with increasing value.
The red circle is the beginning of one period of
sine. Find the x-value of this point.
Average the x-values of the adjacent minimum and
maximum values.
The horizontal shift is .04125 seconds.
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Step 8
Graph the model y k a sin(d(x - h)).
Enter the values found into the function
grapher k 2.6993 v a
0.016 v d 88.185 rad/sec h 0.04125
sec
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Using the TI-83 SinReg function.
Press the STAT key. Use the arrow keys to select
CALC and SinReg. Press ENTER.
Enter the list for the y-values (L2) followed by
a comma.
Press VARS followed by Y-VARS and Function...
Enter the list for the x-values (L1) followed by
a comma.
Enter the function to store the regression. (Y2)
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Using the TI-83 SinReg function.
The screen should now appear similar to
Press ENTER and the calculator will attempt to
determine the regression equation in the form of
y asin(bxc)d. The resulting model is
The model is stored in the function grapher Y2
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Using the TI-83 SinReg function.
The graph will appear similar to
The two models are V 0.016v sin(89.590
rad/sec T sec 2.428 sec) 2.700 v or V
2.699v 0.016v sin(88.185 rad/sec (T sec -
0.041 sec)