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
1) Find the amplitude, period, vertical translation, and phase shift for this function. [Note: the table does not follow the bob through one complete cycle, so some thought will be required to answer this question.]
2) Determine the equation of the function in the form:
h(t) = asin[b(t - c)] + d.
3) What would the rest position of the pendulum be?
4) What is the maximum displacement for this pendulum?
5) The time for one complete cycle is the period. How long would it take to complete 15 cycles?
Sin formula ~
2008-08-20 10:29 am
回答 (2)
2008-08-21 9:17 am
✔ 最佳答案
這題目可能不用這麼複雜的，這裏我用了non-linear optimization找到最優化的sine curve，如果是非大學程度的話可以只用肉眼找parameters：圖片參考：http://i187.photobucket.com/albums/x22/cshung/7008082000336_1.png
圖片參考：http://i187.photobucket.com/albums/x22/cshung/7008082000336_2.png
2008-08-21 01:20:41 補充：
Forget to add, these quantities are in Radians (Except amptitude)
If you need these quantities in degree, you will need to multiply them by 180/pi.
2008-08-21 22:54:08 補充：
The real difficulty is the part of finding parameters.
For high school level, I think it is acceptable to claim you've found this parameters by eye inspection on the plot.
2008-08-21 22:54:20 補充：
For example, it is reasonable to claim both the maximum and minimum are reached and therefore the amptitude is around (55 - 7)/2 = 24, a crude but not bad approximation. The other parameters can be claimed similarly.
I think the parameters I found are quite optimal, you can plot and try :)
參考: 從不抄襲。, 從不抄襲。
2008-08-21 3:19 pm
is there any easier ways to do it? it seems difficult.
this question is from the grade 11 course in canada, thanks
this question is from the grade 11 course in canada, thanks
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