A ball that is bobbing up and down on the end of a spring has a maximum displacement of 3 inches.Its motion (in ideal conditions)is modeled by? $y = \frac { 1 } { 4 } \cos 18 t ( t 0 )$ where y is measured in feet and t is the time in seconds. What is the period of the oscillations?
?
A) $\frac { 9 } { \pi }$
B) $\frac { 18 } { \pi }$
C) $\frac { \pi } { 18 }$
D) $\frac { \pi } { 2 }$
E) $\frac { \pi } { 9 }$

Question

A ball that is bobbing up and down on the end of a spring has a maximum displacement of 3 inches.Its motion (in ideal conditions)is modeled by? $y = \frac { 1 } { 4 } \cos 18 t ( t > 0 )$ where y is measured in feet and t is the time in seconds. What is the period of the oscillations?
?
A) $\frac { 9 } { \pi }$
B) $\frac { 18 } { \pi }$
C) $\frac { \pi } { 18 }$
D) $\frac { \pi } { 2 }$
E) $\frac { \pi } { 9 }$

Quizplus · Accepted Answer

The period of a cosine function of the form $y = A \cos(Bt)$ is given by $T = \frac{2\pi}{B}$. Here, $B = 18$, so the period $T = \frac{2\pi}{18} = \frac{\pi}{9}$.

A Ball That Is Bobbing Up and Down on the End