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. 0.625 seconds 0.8 seconds 1.25 seconds 1.6 seconds

Answer 1

The time it take for the pendulum to swing from its rightmost position to its leftmost position and back again is 1.25 seconds.

What is time period of pendulum?

Pendulum is the body which is pivoted a point and perform back and forth motion around that point by swinging due to the influence of gravity.

The time period of pendulum is time taken by it to complete one cycle of swing left to right and right to left.

The equation models the horizontal distance 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, is given as,

$d = 11 \cos\left( \dfrac{8\pi}{5}t\right)$

At the maximum position, the time period is zero. Thus,

$\dfrac{8\pi}{5}t=0\\t=0$

At the minimum position, the period equal to the π. Thus,

$\dfrac{8\pi}{5}t=\pi\\t=\dfrac{5}{8}\\t=0.625$

This time is for one side of motion. The time for swing from its rightmost position to its leftmost position and back again is,

$t=0.625+0.625\\t=1.25\rm\; s$

Thus, the time it take for the pendulum to swing from its rightmost position to its leftmost position and back again is 1.25 seconds.

Learn more about the time period of pendulum here;

brainly.com/question/3551146

Answer 2

Answer:

C:1.25

Step-by-step explanation: