Yes, a periodic motion can have a changing amplitude. The amplitude of a periodic motion refers to the maximum displacement or magnitude of the oscillation. In many cases, the amplitude remains constant throughout the motion. However, there are situations where the amplitude can vary over time.
One example is a damped harmonic oscillator. In a damped system, such as a mass-spring system with friction or an oscillating pendulum with air resistance, the amplitude gradually decreases over time. The energy of the system is dissipated due to external factors, resulting in a reduction in the amplitude of the oscillations until it eventually comes to a stop.
Another example is an undamped system that is subject to an external force or resonance. In such cases, the amplitude can vary periodically due to the interaction with the external force or the resonance phenomenon. This leads to periodic changes in the amplitude of the oscillation, which can be higher or lower than the initial amplitude.
In summary, while periodic motion typically has a constant amplitude, certain factors such as damping, external forces, or resonance can cause the amplitude to change over time.