Consider an elastic string of length L whose ends are held fixed. The string is set in motion with no initial velocity from an initial position u(x, 0) = f(x). In each of 1 through 4 carry out the following steps. Let L = 10 and a = 1 in parts (b) through (d). (a) Find the displacement u(x, t) for the given initial position f(x). (b) Plot u(x, t) versus x for 0 x 10 and for several values of t between t = 0 and t = 20. (c) Plot u(x, t) versus t for 0 t 20 and for several values of x. (d) Construct an animation of the solution in time for at least one period. (e) Describe the motion of the string in a few sentences.f(x) =1, L/2 1 < x < L/2 + 1 (L > 2),0, otherwise

Here is the definition of the logarithm function. If b is any number such that and and then, We usually read this as “log base b of x”. In this definition is called the logarithm form and is called the exponential form. Note that the requirement that is really a result of the fact that we are also requiring . If you think about it, it will make sense. We are raising a positive number to an exponent and so there is no way that the result can possibly be anything other than another positive number. It is very important to remember that we can’t take the logarithm of zero or a negative number. Now, let’