Answer
The answer is below.
Work Step by Step
The person will infinitely oscillate within the center of the earth. After all, we know that the gravity at earth's surface is large, but we know that the gravity in the exact center of the earth is 0. However, when the person passes through the center of the earth, they will have a considerable velocity, causing them to continue to the other side until gravity slows them down. Consequently, it follows that the person will oscillate.
