Question

The equation d = 11 cosine (startfraction 8 pi over 5 endfraction t) models the horizontal distance, d, in inches of the pendulum of a grandfather clock from the center as it swings from right to left and left to right as a function of time, t, in seconds. according to the model, how long does it take for the pendulum to swing from its rightmost position to its leftmost position and back again? assume that right of center is a positive distance and left of center is a negative distance.

Answer 1

The time that is taken for the pendulum to swing from its rightmost position to its leftmost position and back again is 1.25 seconds

Calculations and Parameters:

Given that this is a cosine equation,

At maximum, Cos (0) =1

At minimum, Cos (π) = -1.

Hence,

At the maximum:

• 8π/5 t = 0
• t = 0

At the minimum:

• 8π/5 t = π
• t = 5/8
• t = 0.625

Given that the time taken from max to min is 0.625 and also to min to max is also 0.625,

The total time taken would be:

0.625 + 0.625 = 1.25s

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