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Pendulum Ride - Trigonometric Function
At Canada's Wonderland, a thrill seeker can ride the Xtreme Skyflyer. This is essentially a large pendulum of which the rider is the bob. The height of the rider is given for various times:
Time(s) 0 1 2 3 4 5 6 7 8 9
Height(m) 55 53 46 36 25 14 7 5 8 15
Find the amplitude, period, vertical translation, and phase shift for this function. [Note: that the table does not follow the bob through one complete cycle, s
y=a sin [b(x-c)] + d
To find "a" (amplitude)= (max - min) / 2 = (55 - 5)/2 = 25
To find "d" (axis of symmetry)= (max + min) / 2 = (55 + 5)/2 = 30
To find "b" find the Period
Period = 2p/absolute value of b
However, because this ride works as a pendulum, one cycle will be completed when there are 2 highs and 2 lows. So the bob starts at a height of 55 metres; it will then reach a low of 5 metres; it will (hypothetically) reach a height until it runs out of speed; it will then (hypothetically) return to the minimum height of 5 metres; and then, finally it will return to its start position. That is the completion of 1 cycle in a pendulum.
Because the graph is incomplete, we have just one maximum and one minimum. The maximum starts at 55 metres, and then there is a minimum at 5 metres. Therefore, we have only completed 1/4 of the cycle at 7 seconds. Roughly, a complete cycle will take 28 seconds.
Therefore Period= 2pie/b
which becomes:
28 seconds = 2pie/b
28=360/b
b=360/28
b=12.86
So the "b" value is 12.86.
To find the value of "c", I will plug in a co-ordinate value into the equation. Let us take the co-ordinate (3, 36)
Therefore:
y=asin[b(x-c)]+d; becomes:
36=25sin[12.86(3-c)]+30
6=25sin[12.86(3-c)]
6/25=sin[12.86(3-c)]
13.89=12.86(3-c)
1.08=3-c
c=3-1.08
c=1.92
And so, my final equation reads as:
y=25sin[12.86(x-1.92)]+30
However, when I enter this value into my graphing software, it looks nothing like the graph I did on paper! Do you guys see any errors in what I did?
Thank you so much in advance.
Homework Statement
At Canada's Wonderland, a thrill seeker can ride the Xtreme Skyflyer. This is essentially a large pendulum of which the rider is the bob. The height of the rider is given for various times:
Time(s) 0 1 2 3 4 5 6 7 8 9
Height(m) 55 53 46 36 25 14 7 5 8 15
Find the amplitude, period, vertical translation, and phase shift for this function. [Note: that the table does not follow the bob through one complete cycle, s
Homework Equations
y=a sin [b(x-c)] + d
The Attempt at a Solution
To find "a" (amplitude)= (max - min) / 2 = (55 - 5)/2 = 25
To find "d" (axis of symmetry)= (max + min) / 2 = (55 + 5)/2 = 30
To find "b" find the Period
Period = 2p/absolute value of b
However, because this ride works as a pendulum, one cycle will be completed when there are 2 highs and 2 lows. So the bob starts at a height of 55 metres; it will then reach a low of 5 metres; it will (hypothetically) reach a height until it runs out of speed; it will then (hypothetically) return to the minimum height of 5 metres; and then, finally it will return to its start position. That is the completion of 1 cycle in a pendulum.
Because the graph is incomplete, we have just one maximum and one minimum. The maximum starts at 55 metres, and then there is a minimum at 5 metres. Therefore, we have only completed 1/4 of the cycle at 7 seconds. Roughly, a complete cycle will take 28 seconds.
Therefore Period= 2pie/b
which becomes:
28 seconds = 2pie/b
28=360/b
b=360/28
b=12.86
So the "b" value is 12.86.
To find the value of "c", I will plug in a co-ordinate value into the equation. Let us take the co-ordinate (3, 36)
Therefore:
y=asin[b(x-c)]+d; becomes:
36=25sin[12.86(3-c)]+30
6=25sin[12.86(3-c)]
6/25=sin[12.86(3-c)]
13.89=12.86(3-c)
1.08=3-c
c=3-1.08
c=1.92
And so, my final equation reads as:
y=25sin[12.86(x-1.92)]+30
However, when I enter this value into my graphing software, it looks nothing like the graph I did on paper! Do you guys see any errors in what I did?
Thank you so much in advance.
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