In simple harmonic motion, the frequency refers to the number of complete oscillations or cycles that occur in a unit of time, while the amplitude represents the maximum displacement or distance from the equilibrium position. The frequency of a simple harmonic motion is determined by the characteristics of the system, such as the mass and stiffness of the object, and is independent of the amplitude.
The reason for the independence of frequency and amplitude lies in the nature of the restoring force that drives the motion. In simple harmonic motion, the restoring force is directly proportional to the displacement but acts in the opposite direction, aiming to restore the system to its equilibrium position. This force is typically given by Hooke's law for springs or an analogous relationship for other systems.
When the displacement from the equilibrium position is small, the restoring force is approximately linear. As a result, the motion becomes harmonic, and the system oscillates with a well-defined frequency determined by its physical properties. The frequency is related to the characteristics of the system, such as the mass and the spring constant (or equivalent parameters), but not to the amplitude.
To understand this concept intuitively, imagine a mass attached to a spring undergoing simple harmonic motion. When the amplitude is increased, the mass will oscillate over a larger distance around the equilibrium position, but the time it takes to complete one cycle remains the same. The frequency of the oscillation remains constant regardless of how far the mass is displaced from the equilibrium.
In summary, the frequency of simple harmonic motion is determined by the properties of the system and is independent of the amplitude. The amplitude affects the extent of the oscillation, but it does not influence the frequency at which the system oscillates.