In an underdamped oscillation, the presence of light damping results in the gradual decrease of the amplitude while the frequency remains relatively constant. This behavior can be explained by considering the effects of damping on the system.
Damping in an oscillatory system arises due to the presence of external forces, such as friction or air resistance, that act to dissipate energy from the system. As the oscillation proceeds, energy is continuously lost to the surroundings, leading to a reduction in the system's total energy.
The decrease in amplitude occurs because the energy dissipated by damping reduces the maximum displacement of the oscillating object over time. As the system loses energy, its ability to reach high magnitudes of displacement diminishes, resulting in a decreasing amplitude.
On the other hand, the frequency of the oscillation remains relatively constant. The frequency is determined primarily by the properties of the system, such as the mass and stiffness of the object undergoing oscillation. While damping affects the motion of the system, it does not significantly alter these inherent properties that determine the frequency.
However, it's important to note that in a damped oscillation, the presence of damping does have a slight influence on the frequency, causing it to decrease gradually over time. This phenomenon is known as the "damped frequency." The decrease in frequency occurs because the damping force acts to slow down the motion of the oscillating object. However, this effect is relatively small for light damping, and the frequency can be considered approximately constant over a reasonable duration of the oscillation.
In summary, in an underdamped oscillation, energy loss due to damping primarily affects the amplitude, causing it to decrease gradually over time. The frequency, while slightly influenced by damping, remains relatively constant for a system with light damping.