Final answer:
Standing on a swing reduces the effective length of the pendulum, shortening the swing's period and causing it to move more quickly back and forth.
Step-by-step explanation:
If a child stands up on the seat of a playground swing, the swing's period will be affected because the effective length of the pendulum, which is the distance from the pivot to the child's center of gravity, changes. When the child stands, this length is reduced compared to when they sit. According to the formula for the period of a simple pendulum, T = 2π√(L/g), where T is the period, L is the effective length, and g is the acceleration due to gravity, the period depends solely on L and g. Thus, with a decreased L when the child stands, the period of the swing will become shorter, causing the swing to move back and forth more quickly. Energy transformation also occurs during swinging; as the swing moves down, the potential energy at the highest points is converted into kinetic energy at the lowest points, and vice versa.