The vertical displacement of a string is given by the harmonic function: y(x, t) = 6cos (16t

The vertical displacement of a string is given by the harmonic function: y(x, t) = 6cos (16πt - 20πx) (m), where x is the horizontal distance along the string in meters. Suppose a tiny particle were to be attached to the string at x = 5 cm, obtain an expression for the vertical velocity of the particle as a function of time.