Bob Goes Faster

Scenario A: Bob attaches a mass mm at the end of a long string (length LL) and holds the other end of the string, allowing the mass to swing like a pendulum, with amplitude AA. When the mass reaches a turning point, Bob quickly pulls on the string so that the swinging part of the string shortens to 12L\tfrac12 L. The pendulum now swings with a higher frequency.

Scenario B: Bob repeats the exact same situation: a pendulum length LL and mass mm is swinging with amplitude AA. This time, Bob quickly pulls on the string when the mass passes through the equilibrium position. Again, the string is shortened to 12L\tfrac12 L, and the pendulum swings with a higher frequency.

In which scenario, if any, will the pendulum have a greater amplitude after Bob shortens the string?

Assumptions: The size of the swinging mass is negligible. When Bob pulls on the string, he does this in a negligible amount of time. During the pull, the force is directed upward along the string.

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