PHYS2113 2023 Video 9 -- Lagrange Multipliers

[@peterwan9076]

In the very last pendulum example, the y component of the tension should act in opposite direction to the weight (mg). But in your FT_y equation, the y component of the tension is in the same direction of the weight. It does NOT make sense then? The weight minus the y component of the tension should be responsible for the vertical acceleration. But your FT_y equation does NOT reflect that. I believe the Lagrange multiplier method gives the "magnitude" of the constraint force only and we have to determine the sign ourselves using common sense.

[@rhinexiang7207]

acceleration in y will always be smaller than g (acceleration without string/constraint) in a pendulum, so the FT_y will be negative, and because the y axis is set up to point down when positive, the tension_y is opposite in direction to mg