Solve the problem.
-Determine the length of a pendulum that has a period of 2 seconds.
A) $\frac { \pi } { 2 } \mathrm { ft }$
B) $\frac { \pi ^ { 2 } } { 16 } \mathrm { ft }$
C) $\frac { \pi } { 4 } \mathrm { ft }$
D) $\frac { 32 } { \pi ^ { 2 } } \mathrm { ft }$

Question

Quizplus · Accepted Answer

The period $T$ of a pendulum is given by $T = 2\pi\sqrt{\frac{L}{g}}$, where $L$ is the length of the pendulum and $g$ is the acceleration due to gravity ($9.8 \, \text{m/s}^2$ or approximately $32 \, \text{ft/s}^2$ for calculations in feet). Given $T = 2$ seconds, we can solve for $L$:$$2 = 2\pi\sqrt{\frac{L}{32}}$$Squaring both sides and solving for $L$ gives:$$L = \frac{32}{\pi^2}$$

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Solve the Problem $\frac { \pi } { 2 } \mathrm { ft }$