Consider the small amplitude vibrations of the uniform string below. The string is fixed at both ends and has an intermediate spring $k$ attached at $x = x_{0}$ . Question 1 Write down the governing equation(s) and the necessary boundary conditions. Write down the characteristic equation for this system. What simple check(s) could you use to verify that your answer is correct? (25 pts)

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Consider the small amplitude vibrations of the uniform string below. The string is fixed at both ends and has an intermediate spring

k

attached at

x = x_{0}

. Question 1 Write down the governing equation(s) and the necessary boundary conditions. Write down the characteristic equation for this system. What simple check(s) could you use to verify that your answer is correct? (25 pts)

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