Final answer:
Oscillations with a frequency that varies with amplitude cannot be considered simple harmonic motion because SHM requires the frequency to be constant, regardless of amplitude. Examples of SHM include a mass on a spring, while large-amplitude pendulum swings may have frequency depending on their amplitude.
Step-by-step explanation:
If the frequency of some oscillation is not constant, then the oscillation cannot be considered simple harmonic motion (SHM). One of the defining characteristics of simple harmonic motion is that the frequency and period of oscillation are independent of the amplitude. Therefore, an oscillation where the frequency varies with amplitude does not meet the criteria for SHM.
An example of a simple harmonic oscillator is a mass on a spring, which oscillates at a frequency that is determined by the mass and the stiffness of the spring, and not by the amplitude of oscillation. However, a real-world example where frequency may depend on amplitude is a large-amplitude pendulum; in such cases, the restoring force does not remain strictly proportional to the displacement, leading to a deviation from the true simple harmonic motion.