Pendulum Wall Clock
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which math formulas to use, arithmetic sequences, arithmetic series, geometric sequences, geometric series?
The spring in Juanita's old grandfather clock is broken. When you try to set the pendulum in motion by holding it against the wall of the clock and letting go, it follows a swing pattern of 25 cm, 16 cm, and so on until it comes to rest.
a) What is the distance it will swing on the 10th swing?
b) What is the total distance it will swing after 10 swings?
c) What is the total distance it will travel before coming to a stop?
Which formula do I use: arithmetic sequence, arithmetic series, geometric sequence, and/or geometric series?
Here we have,
The swings are : 25, 25(16/25), 25(16/25)^2, 25(16/25)^3, . .............
Here first term, a = 25
common ratio, r = 16/25
a)
The distance it will swing on the 10th swing is :
T10 = a.(r)^9 = 25(16/25)^9 = 0.4504 cm. ................................... Answer
b)
The total distance it will swing after 10 swings is :
S10 = a(1 - r^10) / (1 - r) = 25(1 - (16/25)^10) / (1 - 16/25) =
S10 = 25*0.9885 / 0.36 = 68.646 cm. ...................................... Answer
c)
The total distance it will travel before coming to a stop is :
S = a / (1-r) = 25 / (1-16/25) = 39.0625 cm. ......................... Answer
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