A weight attached to a spring is at its lowest point, 9 inches below equilibrium, at time t is equal to 0 seconds. When the weight is released, it oscillates and returns to its original position at t is equal to 3 seconds. Which of the following equations models the distance, d , of the weight from its equilibrium after t seconds?
Answer
A
d is equal to negative 9 cosine open paren pi over 3 t close paren
B
d is equal to negative 9 cosine open paren 2 pi over 3 t close paren
C
d is equal to negative 3 cosine open paren pi over 9 t close paren
D
d is equal to negative 3 cosine open paren 2 pi over 9 t close paren
Explanation
At t = 0, the weight is 9 inches below equilibrium, so its displacement is −9 inches. Since it returns to its original position after 3 seconds, the period is 3, giving angular frequency 2π/3. The model is therefore d = −9 cos((2π/3)t), which is choice B.
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