The boundaryvalue problem for a clampedclamped beam can be written as

When a uniformly distributed load is applied, that is, \(p(x)=p_{0}\), calculate the approximate beam deflection \(\tilde{w}(x)\) using the Galerkin method. Hint: Assume the approximate deflection as \(\tilde{w}(x)=c \phi(x)=c x^{2}(1-x)^{2}\).

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d'w d4-P(x)=0, 0x 1 dw dw w(0) = w(1)= (0) = d(1)=0) boundary conditions. dr dx