It messes up the math.
For large amplitude swings, the simple relation that the period of a pendulum is directly proportional to the square root of the length of the pendulum (only, assuming constant gravity) no longer holds. Specifically, the period increases with increasing amplitude.
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it doesn't
The period of a pendulum is (sort of) independent of the amplitude. This is technically true for very small, "infinitesimal" swings. In this range, amplitude does not affect period. For larger swings, however, a circular error is introduced, but it is possible to compensate with various designs. See the Related Link below for further information.
The amplitude of a pendulum is the distance between its equilibrium point and the farthest point that it reaches during each oscillation.
The pendulum swings twice as far.
That if the original amplitude was A then it is now 2*A.