Respuesta :
The cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds) is d(t) = 6cos([tex]\pi[/tex]t).
What is the principle of pendulum?
As long as its length is constant, a pendulum completes each swing (or oscillation) in precisely the same amount of time. Any particular pendulum oscillates for a fixed amount of time.
Calculation for the cosine function-
The given function is: cosine function, d = acos(bt).
As, the pendulum 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.
The total time 't' by the pendulum is 2 sec.
Calculate the angular speed of the pendulum by-
ω = 2[tex]\pi[/tex]f
= 2[tex]\pi[/tex]×(1/2)
ω = [tex]\pi[/tex] which is 'b' value of the given function.
As given, the distance of the pendulum from the centre is half of the total distance.
a = 12/2
a = 6
Substitute the obtained values in the cosine function, d = acos(bt),
d(t) = 6cos([tex]\pi[/tex]t)
Therefore, the cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds) is d(t) = 6cos([tex]\pi[/tex]t).
To know more about the basic principle of the pendulum, here
https://brainly.com/question/13868386
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The complete question is -
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 = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds).
