Final answer:
A mass-spring system is an example of a simple harmonic oscillator with a frequency that is independent of amplitude, which is unique to simple harmonic motion (SHM). The frequency in SHM only depends on the mass and the spring constant, not on the oscillation's amplitude. This constant frequency makes SHM ideal for applications such as timekeeping.
Step-by-step explanation:
An example of a simple harmonic oscillator where the frequency is independent of amplitude is a mass-spring system. In this system, a mass is attached to a spring and the other end of the spring is attached to a rigid support. According to Hooke's law, the restoring force exerted by the spring on the mass is proportional to the displacement from its equilibrium position, but the frequency of the oscillations only depends on the mass and the spring constant, not on the amplitude of the oscillations.
The conditions that must be met to produce simple harmonic motion (SHM) include: the restoring force must be directly proportional to the displacement and directed towards the equilibrium position, and the system must have the capacity for inertia. If the frequency of the oscillations varies with amplitude, the motion cannot be considered SHM. Though the pendulum is often considered a simple harmonic oscillator, at larger amplitudes, the frequency can become dependent on the amplitude, which deviates from SHM.
One of the significant aspects of simple harmonic motion is that it is periodic and the period and frequency are constants, making it ideal for precise measurements like timekeeping in clocks.