Answer:
The time it takes for the pendulum to swing from its rightmost position to its leftmost position and back again is 1.25 seconds.
Step-by-step explanation:
Given the equation
[tex]d = 11cos( \frac{8\pi}{5}*t)[/tex]-----------Equation 1
where d, in inches of the pendulum of a grandfather clock from the center.
Comparing with the standard equation of an oscillating pendulum bob.
[tex]d = Acos (wt + \alpha )[/tex] ----------Equation 2
where ω = angular velocity
t = time taken
α = The angular displacement when t = 0
Comparing equation 1 and 2,
α = 0
[tex]w =\frac{8\pi }{5}[/tex]
Recall that [tex]w = 2\pi f
Therefore,
[tex]2\pi f = \frac{8\pi }{5} \\\\f = \frac{4}{5}[/tex][/tex]
f = 0.8 Hertz
Recall that [tex]f = \frac{1}{T}[/tex]
[tex]T = \frac{1}{0.8}[/tex]
T = 1.25 seconds
Therefore, the time it takes for the pendulum to swing from its rightmost position to its leftmost position and back again is 1.25 seconds.
