Consider the uniform bar in the figure. Axial load \(q\) is linearly distributed along the length of the bar according to \(q=c x\), where \(c\) is a constant that has units of force divided by the square of length. Calculate the axial displacement \(u(x)\) and axial stress \(\sigma_{x}\) using the RayleighRitz method. Assume the following form of displacement: \(\quad u(x)=a_{0}+a_{1} x\).

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E, A q = cx L X, U