# Wave Equation : Finite String and Maximum Displacement

Q Ut4iOE) 3

A finite string of length L that is fixed at both ends and is released from rest with an initial displacement will have the following mathamatical description by the wave equation

U =a^2 Uxx

Given a = 30 m/s and the initial velocity of 300sin(4 pi x) from Its equilibrium position and L = 4m. find the solution for the displacement. What is the maximum displacement? Clearly indicate each step of your working. If the length is reduced to 2m, what will the effect on the maximium displacement?

See the attached file.

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A wave equation, finite string and maximum displacement are investigated and discussed in the solution. The solution is detailed and well presented.