starting at its rightmost position, it takes 1 second for the pendulum of a grandfather clock to swing a…

starting at its rightmost position, it takes 1 second for the pendulum of a grandfather clock to swing a horizontal distance of 12 inches from right to left, and 1 second for the pendulum to swing back from left to right. write a cosine function, $d = a\\cos(bt)$, to model the distance, $d$, of the pendulum from the center (in inches) as a function of time $t$ (in seconds).\na = 6\ncomplete\nthe period is \nseconds.\nb =\ndone

starting at its rightmost position, it takes 1 second for the pendulum of a grandfather clock to swing a horizontal distance of 12 inches from right to left, and 1 second for the pendulum to swing back from left to right. write a cosine function, $d = a\\cos(bt)$, to model the distance, $d$, of the pendulum from the center (in inches) as a function of time $t$ (in seconds).\na = 6\ncomplete\nthe period is \nseconds.\nb =\ndone

Answer

Answer:

The period is 2 seconds. $b=\pi$

Explanation:

Step1: Determine the period

The pendulum takes 1 second to swing from right - to - left and 1 second to swing from left - to - right. So the period $T$ (time for one full back - and - forth motion) is $1 + 1=2$ seconds.

Step2: Find the value of $b$

The formula for the period of a cosine function $y = a\cos(bt)$ is $T=\frac{2\pi}{b}$. We know $T = 2$. Substituting $T$ into the formula gives $2=\frac{2\pi}{b}$. Solving for $b$: [ \begin{align*} 2b&=2\pi\ b&=\pi \end{align*} ]