Question

The time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation below.

f (l) = 2 pi StartRoot StartFraction l Over 32 EndFraction EndRoot, where l is the length of the pendulum in feet

What is the approximate length of a pendulum that takes 2.4 pi seconds to swing back and forth?
1.72 ft
3.05 ft
38.40 ft
46.08 ft

Answer 1

2π√(l/32) = 2.4π
⇒ 2√(l/32) = 2.4 (divide both sides by π)
⇒ √(l/32) = 1.2 (divide by 2)
⇒ l/32 = 1.44 (square both sides)
⇒ l = 32 × 1.44 = 46.08

Answer: 46.08 ft.