Starting at its rightmost position, it takes 2 seconds for the pendulum of a grandfather clock to swing a horizontal distance of 18 inches from right to left and 2 seconds for the pendulum to swing back from left to right. Which of the following equations models d , the horizontal distance in inches of the pendulum from the center as a function of time, t , in seconds? Assume that right of center is a positive distance and left of center is a negative distance.
Answer
A
d is equal to 18 cosine open paren pi over 2 t close paren
B
d is equal to 9 cosine open paren pi over 4 t close paren
C
d is equal to 9 cosine open paren pi over 2 t close paren
D
d is equal to 18 cosine open paren pi over 4 t close paren
Explanation
The pendulum moves 18 inches from its rightmost position to its leftmost position, so its distance from the center ranges from +9 inches to −9 inches. Thus the amplitude is 9. That trip takes 2 seconds, which is half a cycle, so the full period is 4 seconds and the angular frequency is 2π/4 = π/2. Since it starts at the rightmost position, a cosine model is appropriate: d = 9 cos(πt/2), choice C.
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