No, a function with decreasing amplitude, such as in a damped oscillation, is generally not periodic in the strict sense.
In a damped oscillation, the amplitude of the oscillatory motion decreases over time due to the dissipation of energy. This typically occurs in systems subject to damping forces, such as friction or air resistance. As the energy of the system is gradually lost, the amplitude of the oscillations diminishes until the motion eventually ceases.
Periodicity, on the other hand, refers to the property of a function or waveform that repeats itself identically at regular intervals. In a periodic function, the pattern of the waveform repeats after a certain period, and this behavior continues indefinitely.
In the case of a damped oscillation, the decreasing amplitude prevents the waveform from repeating itself exactly at regular intervals. Although there may be some resemblance or similarity between subsequent cycles, the diminishing amplitude prevents the oscillation from being strictly periodic.
It's worth noting that there are other types of oscillations and waveforms that exhibit damping or attenuation while maintaining periodicity, such as underdamped oscillations. In these cases, the amplitude gradually decreases, but the waveform still repeats at regular intervals. However, in the context of a damped oscillation with decreasing amplitude, periodicity is not typically preserved.