Solve the problem.
-A guitar string is plucked so that it vibrates with a frequency of F = 66. Suppose the maximum displacement at the center of the string is s(0)= 0.58. Find an equation of the form s(t)= a cos bt to
Model this displacement. Round constants to 2 decimal places.
A)s(t)= 0.58 cos 414.69t
B)s(t)= 0.58 cos 10.50t
C)s(t)= 1.16 cos 414.69t
D)s(t)= 1.16 cos 10.50t

Question

Quizplus · Accepted Answer

The equation for the displacement of a vibrating string can be modeled as $s(t) = a \cos(bt)$, where $a$ is the maximum displacement, and $b$ is related to the frequency of vibration. Given $a = 0.58$ (the maximum displacement) and the frequency $F = 66$, we can find $b$ by using the relation $b = 2\pi F$. Calculating $b = 2\pi \times 66 \approx 414.69$, the equation becomes $s(t) = 0.58 \cos(414.69t)$.

Solve the Problem. -A Guitar String Is Plucked So That It Vibrates with It