No, the frequency of an oscillating system does not depend on the amplitude of the motion. The frequency remains constant regardless of the amplitude in simple harmonic motion or any other type of periodic motion.
The frequency of an oscillation refers to the number of complete cycles or oscillations that occur per unit of time. It is typically denoted by 'f' and is measured in hertz (Hz). The frequency is inversely related to the period (T) of the oscillation:
f = 1/T
The period represents the time it takes for one complete cycle, while the frequency measures the number of cycles per unit of time. They are reciprocals of each other.
In simple harmonic motion (SHM), the frequency is determined by the characteristics of the system, such as the mass and the spring constant (in the case of a mass-spring system) or the length of the pendulum (in the case of a pendulum). It is not affected by the amplitude of the motion.
Changing the amplitude of the motion in SHM only affects the range or magnitude of the oscillation. It determines how far the object moves from its equilibrium position. However, it does not alter the frequency of the oscillation. The system will still complete the same number of cycles in the same amount of time regardless of the amplitude.