Solve the problem.
-A guitar string is plucked so that it vibrates with a frequency of $F = 60$. Suppose the maximum displacement at the center of the string is $s ( 0 ) = 0.53$. Find an equation of the form $s ( t ) = a \cos b t$ to model this displacement. Round constants to 2 decimal places.
A) $\mathrm { s } ( \mathrm { t } ) = 1.06 \cos 376.99 \mathrm { t }$
B) $\mathrm { s } ( \mathrm { t } ) = 0.53 \cos 376.99 \mathrm { t }$
C) $s ( t ) = 0.53 \cos 9.55 \mathrm { t }$
D) $s ( t ) = 1.06 \cos 9.55 t$

Question

Quizplus · Accepted Answer

The equation for the displacement of a vibrating string can be modeled as $s(t) = a \cos(b t)$, where $a$ is the amplitude and $b$ is the angular frequency. The amplitude $a$ is given as the maximum displacement, which is 0.53. The angular frequency $b$ can be calculated from the frequency $F$ using the formula $b = 2\pi F$. Given $F = 60$, we find $b = 2\pi \times 60 = 376.99$. Therefore, the correct model is $s(t) = 0.53 \cos(376.99 t)$.

Solve the Problem F=60F = 60F=60 Suppose the Maximum Displacement at the Center of the It

Solve the Problem $F = 60$ Suppose the Maximum Displacement at the Center of the It