Solve the problem.
-The period of vibration P for a pendulum varies directly as the square root of the length L. If the period of vibration is 2 sec when the length is 16 inches, what is the period when L = 1.5625 inches?
A) 2.5 sec
B) 0.625 sec
C) 2.75 sec
D) 3 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 the constant of proportionality. Given $P = 2$ sec when $L = 16$ inches, we can find $k$ by substituting these values into the equation: $2 = k\sqrt{16}$, which simplifies to $2 = 4k$, so $k = 0.5$. For $L = 1.5625$ inches, $P = 0.5\sqrt{1.5625} = 0.5 \times 1.25 = 0.625$ sec.

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