A string is stretched between two posts with the equilibrium position of the string lying along the x-axis. After the string is plucked, let z = s(x, t) denote the vertical displacement of the string at position z and time t. 2 string plucked string s t Os r equilibrium 1. Give a short interpretation, in words, of each of the following quantities: i) The function s(z,0). ii) The partial derivative iii) The partial derivative iv) The second partial derivative v) The second partial derivative 812 ^x 2. For a particular string, we have s(x, t)=4-(-2 (a) Find and (b) Sketch graphs of s(x,0), s(z. 1), s(r, 2) and s(r, 3). (e) The previous part should convince you that this particular s(x, t) is a travelling wave', going from left to right. Modify the equation for s to find an equation that describes the same wave, but traveling from right to left.