What characterises simple harmonic motion (SHM)?

Simple harmonic motion (SHM) is characterised by oscillations about an equilibrium position with a constant amplitude and period.

In more detail, simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement. This means that the object will always be pulled back towards the equilibrium position, and the force pulling it back will be stronger the further it is from this position. The motion is sinusoidal in time and demonstrates a single resonant frequency.

The key characteristics of SHM include a constant amplitude, which is the maximum distance from the equilibrium position, and a constant period, which is the time taken for one complete cycle of motion. The frequency, which is the number of cycles per unit of time, is also constant and is the reciprocal of the period.

In SHM, the velocity of the object varies, being maximum at the equilibrium position and zero at the extremes of the motion. The acceleration is also variable, being zero at the equilibrium position and maximum at the extremes of the motion. This acceleration is always directed towards the equilibrium position, which is why the object oscillates back and forth.

The energy in SHM is conserved, oscillating between potential and kinetic energy. At the extremes of the motion, all the energy is potential, and at the equilibrium position, all the energy is kinetic.

Examples of SHM include the motion of a simple pendulum (for small angles), a mass on a spring, and the oscillations of a tuning fork. These systems all exhibit the key characteristics of SHM: a restoring force proportional to displacement, constant amplitude and period, and energy conservation.

In summary, simple harmonic motion is a fundamental concept in physics, characterised by its constant amplitude and period, and the sinusoidal nature of its oscillations. It is a model that describes many physical systems, from pendulums to atomic vibrations.