The end of a tuning fork moves in simple harmonic motion described by the equation d = a sin (ωt). If a tuning fork for the note A above middle C on an even tempered scale (A₄, the tone by which an orchestra tunes itself) has a frequency of 440 hertz (cycles per second), find ω. If the maximum displacement of the end of the tuning fork is 0.01 millimeter, determine the equation that describes the movement of the tuning fork.