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 3.5 sec when the length is 49 inches, what is the period when L = 1.5625 inches?
A) 3.75 sec
B) 0.625 sec
C) 4.25 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 $P = k\sqrt{L}$ for some constant $k$. Given $P = 3.5$ sec when $L = 49$ inches, we find $k$ by substituting these values: $3.5 = k\sqrt{49}$, which simplifies to $3.5 = 7k$, 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 Period of Vibration P for a Pendulum Varies Directly