Function which describe the motion of the pendulum is called the function of the pendulum. The cosine function of the pendulum is,
\(d(t)=6\cos (\pi t)\)
What is the function of the pendulum?
Function which describe the motion of the pendulum is called the function of the pendulum.
Given information-
The given cosine function for the pendulum is,
\(d=a\cos (bt)\)
The pendulum takes 1 second to swing horizontal distance of 12 inches from right to left.
The pendulum takes 1 second to swing horizontal distance of 12 inches from left to right.
The total time taken by the pendulum to complete one cycle is,
\(t=1+1\\t=2\)
Thus the time taken by the pendulum to complete one cycle is 2 seconds.
As the frequency of the pendulum is inverse of the time. Thus frequency,
\(f=\dfrac{1}{t} \\f=\dfrac{1}{2}\)
Angular speed of the pendulum can be given as,
\(\omega=2\pi f\\\omega=2\times\pi\times\dfrac{1}{2} \\\omega=\pi\)
Thus value of angular acceleration \(b\) is \(\pi\) red per seconds.
The distance of the pendulum from the center is half of the total distance. Thus,
\(a=\dfrac{12}{2} \\a=6\)
Hence the distance of the pendulum from the center is 6 inch.
Put the value in given cosine function as,
\(d(t)=6\cos (\pi t)\)
Thus the cosine function of the pendulum is,
\(d(t)=6\cos (\pi t)\)
Learn more about the function of pendulum here;
https://brainly.com/question/3444989
