# Bob Goes Faster

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

Scenario B: Bob repeats the exact same situation: a pendulum length $$L$$ and mass $$m$$ is swinging with amplitude $$A$$. This time, Bob quickly pulls on the string when the mass passes through the equilibrium position. Again, the string is shortened to $$\tfrac12 L$$, 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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