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Finding the displacement y(x,t) to the string at any point at any subsequent time described by a function .
A semi infinite string is initially at rest in a position co-inciting with the position half of the x-axis.
At t=0, the left end of the string begins to more along the y-axis in a manner described by y(o,t)= f(x) , where f(x) is a known function. Find the displacement y(x, t) of the string at any point at any subsequent time. The problem may be stated as follows:
And y(0,t) = f(x), y(x,t) is bounded as x → ∞ , y(x,0) = 0, yt(x,0) = 0, special case f(x) = et
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