Question: 4 . 2 8 The uniform beam shown is simply supported and is loaded by moment ( M _ { o } )

4.28 The uniform beam shown is simply supported and is loaded by moment \( M_{o}\) at its left end.
(a) Write an equation that constrains the two end rotations to be of equal magnitude but opposite sign.
(b) Solve for the end rotation by means of a Lagrange multiplier.
(c) Solve for the end rotation by means of the penalty method.
4 . 2 8 The uniform beam shown is simply

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