Final answer:
The pendulum's original energy is proportional to its height. After 3 minutes, the energy is reduced to a fraction corresponding to the reduced amplitude of the swing, which is 2/5 or 40% of the original energy.
Step-by-step explanation:
To determine what fraction of the pendulum's original energy remains after 3 minutes, we should consider the principle of conservation of mechanical energy in a pendulum's swing, assuming no non-conservative forces like air resistance or friction. The mechanical energy in a pendulum consists of potential and kinetic energy. When the pendulum is released from a height, it has maximum potential energy and minimum kinetic energy. As it swings down, potential energy is converted into kinetic energy. The highest point in the swing corresponds to the maximum potential energy.
At the start, the pendulum was released at an arc length of 5 m, which we can refer to as the amplitude of the swing. After 3 minutes, the amplitude is reduced to 2 m. The potential energy of a pendulum is directly proportional to its height. Assuming that the amplitude correlates proportionally with height, we can say that if the pendulum's energy was E at the start, at 3 minutes, with the amplitude reduced to 2 m, the energy would be (2/5) of E due to the reduced height.
The fraction of the pendulum's original energy remaining after 3 minutes is (2/5) which can be expressed as 40%. Therefore, 40% of the pendulum's original energy remains.