In simple harmonic motion (SHM), the relationship between frequency and amplitude is inversely proportional. As the frequency of the motion increases, the amplitude decreases, and vice versa.
The reason for this relationship can be understood by considering the underlying principles of SHM. In SHM, an oscillating system experiences a restoring force that is directly proportional to its displacement from the equilibrium position and acts in the opposite direction. This restoring force is typically described by Hooke's law, which states that the force is proportional to the displacement.
When a system is subjected to SHM, it has a natural frequency at which it oscillates most easily. This natural frequency is determined by the system's mass and the characteristics of the restoring force (e.g., the stiffness of a spring). At this natural frequency, the system oscillates with maximum amplitude.
Now, let's consider the relationship between frequency and amplitude in SHM:
Higher Frequency, Lower Amplitude: When the frequency of the oscillating system increases, the time available for each complete oscillation decreases. As a result, the system has less time to reach its maximum displacement during each cycle. Therefore, the amplitude of the motion decreases as the frequency increases.
Lower Frequency, Higher Amplitude: Conversely, when the frequency of the oscillating system decreases, the time available for each complete oscillation increases. This longer time allows the system to reach a larger displacement during each cycle, leading to a higher amplitude of motion.
In summary, the relationship between frequency and amplitude in simple harmonic motion is inversely proportional. Higher frequencies correspond to lower amplitudes, while lower frequencies correspond to higher amplitudes. This relationship arises from the fundamental properties of SHM, where the system's natural frequency and the available time for oscillation influence the extent of displacement.