the equation $d = 11\\cos(\\frac{8\\pi}{5}t)$ models the horizontal distance, $d$, in inches of the pendulum…

the equation $d = 11\\cos(\\frac{8\\pi}{5}t)$ 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.\n0.625 seconds\n0.8 seconds\n1.25 seconds\n1.6 seconds

the equation $d = 11\\cos(\\frac{8\\pi}{5}t)$ 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.\n0.625 seconds\n0.8 seconds\n1.25 seconds\n1.6 seconds

Answer

Answer:

1.25 seconds

Explanation:

Step1: Identify the function form

The given function is $d = 11\cos(\frac{8\pi}{5}t)$, which is a cosine - type function of the form $y = A\cos(\omega t)$.

Step2: Recall the period formula

The period $T$ of a cosine function $y = A\cos(\omega t)$ is given by $T=\frac{2\pi}{\omega}$.

Step3: Determine the value of $\omega$

In the function $d = 11\cos(\frac{8\pi}{5}t)$, $\omega=\frac{8\pi}{5}$.

Step4: Calculate the period

Substitute $\omega=\frac{8\pi}{5}$ into the period formula $T = \frac{2\pi}{\omega}$. So $T=\frac{2\pi}{\frac{8\pi}{5}}$.

Step5: Simplify the expression

$T=\frac{2\pi\times5}{8\pi}=\frac{10\pi}{8\pi}=\frac{5}{4}=1.25$ seconds. The time it takes for the pendulum to swing from its right - most position to its left - most position and back again is one period of the cosine function.