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A simple pendulum of length 4.19742 meters starts from rest and swings down from an unknown...

A simple pendulum of length 4.19742 meters starts from rest and swings down from an unknown angle. When it is vertical, it smashes into a peg at the midpoint of its length. The pendulum then swings across to the other side and becomes exactly horizontal at its turnaround point. It then swings back to its original location.

Determine the time it takes to do so. Be as exact as possible.

Hint #1: Do not use the formula for the period of a small-angle pendulum. See the lab on this topic.

Hint #2: Use conservation of energy and trigonometry to determine the initial angle

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