Chapter 8.5, Problem 56AYU

Tuning Fork The end of a tuning fork moves in simple harmonic motion described by the equation $d=a\sin (\omega t)$. If a tuning fork for the note $E$ above middle $C$ on an even-tempered scale $\left(E_4\right)$ has a frequency of approximately $329.63$ hertz (cycles per second), find $\omega$. If the maximum displacement of the end of the tuning fork is $0.025$ millimeter, determine the equation that describes the movement of the tuning fork.

Source: David Lapp. Physics of Music and Musical Instruments. Medford, MA: Tufts University, 2003