Solve the problem.
-Determine the length of a pendulum that has a period of 4 seconds.
A) $\frac { 128 } { \pi ^ { 2 } } \mathrm { ft }$
B) $\frac { \pi } { 8 } \mathrm { ft }$
C) $\frac { \pi } { 4 } \mathrm { ft }$
D) $\frac { \pi ^ { 2 } } { 32 } \mathrm { ft }$

Question

Solve the problem.
-Determine the length of a pendulum that has a period of 4 seconds. 
A) $\frac { 128 } { \pi ^ { 2 } } \mathrm { ft }$
B) $\frac { \pi } { 8 } \mathrm { ft }$
C) $\frac { \pi } { 4 } \mathrm { ft }$
D) $\frac { \pi ^ { 2 } } { 32 } \mathrm { ft }$

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 (approximately $32 \, \text{ft/s}^2$ in this context). Rearranging for $L$, we get $L = \frac{gT^2}{4\pi^2}$. Substituting $T = 4$ seconds and $g = 32 \, \text{ft/s}^2$, we find $L = \frac{32 \times 16}{4\pi^2} = \frac{128}{\pi^2} \, \text{ft}$.

Solve the Problem 128π2ft\frac { 128 } { \pi ^ { 2 } } \mathrm { ft }π2128​ft

Solve the Problem $\frac { 128 } { \pi ^ { 2 } } \mathrm { ft }$