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2. Consider an elastic string that is stretched to length L = 2 and endpoints fixed. Suppose that the initial deflection of the string is zero and the initial velocity is given by a function with the following function: g(x) = {2x - (2x2x² 0 for 0 < x < 1 for 1 < x < 2 Using the method of separation of variables, solve for the deflection u(x, t) of the string. Show the details of your calculation. Write explicitly at least the first three non-vanishing terms in u(x, t). You may assume that the separation constant k = -q² < 0, for q> 0, from the outset. [20 marks]