Chapter 6.4, Problem 47PE

Suppose that a guitar string is plucked such that the center of the string is initially displaced $10\text{ mm}$ and then vibrates under damped harmonic motion. The note produced has a frequency of $110\text{ Hz}$ . The note is no longer audible to a normal human ear once the displacement at the middle of the string is less than $0.1\text{ mm}$ . What is the damping factor if the sound is no longer audible after $2.5\text{ sec}$ ? Round to $2$ decimal places.