Determine the equation of the graph.
-Determine the period and frequency of oscillation when a pendulum of length 7 feet is released after being displaced 2 radians. Round constants to 8 decimal places, if necessary.
A) Period $= 2 \pi \sqrt { 0.21875 }$ sec, frequency $= \frac { 1 } { 2 \pi } \sqrt { 4.57142857 }$ cycles per sec
B) Period $= 2 \pi \sqrt { 4.57142857 }$ sec, frequency $= \frac { 1 } { 2 \pi } \sqrt { 0.21875 }$ cycles per sec
C) Period $= 7 \pi \mathrm { sec }$, frequency $= \frac { 1 } { 7 \pi }$ cycles per sec
D) Period $= \frac { \pi } { 7 }$ sec, frequency $= \frac { 7 } { \pi }$ cycles per sec

Question

Quizplus · Accepted Answer

The period 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. In this case, $ L = 7 $ feet and $ g = 32 $ feet per second squared, so the period is $ T = 2 \pi \sqrt { \frac { 7 } { 32 } } $ seconds. The frequency of a pendulum is given by $ f = \frac { 1 } { T } $, so the frequency in this case is $ f = \frac { 1 } { 2 \pi \sqrt { \frac { 7 } { 32 } } } $ cycles per second.

Determine the Equation of the Graph =2π0.21875= 2 \pi \sqrt { 0.21875 }=2π0.21875​

Determine the Equation of the Graph $= 2 \pi \sqrt { 0.21875 }$