Solve the problem. Round your answer to two decimal places.
-The period of vibration P for a pendulum varies directly as the square root of the length L. If the period of vibration is 4 sec when the length is 64 inches, what is the period when L = 5.0625
Inches?
A) 5 sec
B) 1.125 sec
C) 4.5 sec
D) 4.75 sec

Question

Quizplus · Accepted Answer

The period of vibration $P$ is directly proportional to the square root of the length $L$, so $P = k\sqrt{L}$, where $k$ is a constant. Given $P = 4$ sec when $L = 64$ inches, we can find $k$ by substituting these values: $4 = k\sqrt{64}$, which simplifies to $4 = k*8$, so $k = 0.5$. For $L = 5.0625$ inches, $P = 0.5\sqrt{5.0625} = 0.5*2.25 = 1.125$ sec.

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