No, periodic motion does not necessarily have the same amplitude over all time intervals. The amplitude of periodic motion refers to the maximum displacement or magnitude of the oscillation from the equilibrium position.
In many periodic systems, such as simple harmonic motion, the amplitude remains constant over time. For example, in a pendulum swinging back and forth, the amplitude would remain the same if there are no external factors affecting it.
However, there are cases where the amplitude can change over time. This can occur in certain types of periodic motion that are influenced by external factors or have nonlinear behaviors. Some examples include damped oscillations, forced oscillations, or systems with amplitude modulation.
In damped oscillations, the amplitude gradually decreases over time due to the dissipation of energy, such as in a swinging pendulum experiencing air resistance.
Forced oscillations occur when an external force or input is applied to a system, causing it to oscillate with a specific frequency. In such cases, the amplitude of the resulting motion can depend on the properties of the driving force and the resonant characteristics of the system.
Amplitude modulation refers to a periodic motion where the amplitude itself varies periodically. This can be observed in certain types of waves, such as modulated signals in communication systems.
Therefore, while the concept of amplitude is important in describing periodic motion, it can vary over time depending on the specific characteristics and influences on the system.