Solve.
-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)4.25 sec
B)5 sec
C)1.125 sec
D)4.5 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: $4 = k\sqrt{64}$, so $k = 4/8 = 0.5$. For $L = 5.0625$ inches, $P = 0.5\sqrt{5.0625} = 0.5 \times 2.25 = 1.125$ sec.

Solve. -The Period of Vibration P for a Pendulum Varies Directly