Simple Harmonic Motion (SHM) is a type of periodic motion in which an object oscillates back and forth around an equilibrium point under the influence of a restoring force that is directly proportional to the displacement from the equilibrium point.
The conditions for Simple Harmonic Motion are that the restoring force must be directly proportional to the displacement from the equilibrium point, and the motion must be periodic and repeat itself in a regular pattern.
The equation for Simple Harmonic Motion is x(t) = A sin(ωt + φ), where x(t) is the displacement at time t, A is the amplitude (maximum displacement), ω is the angular frequency (related to the period of the motion), and φ is the phase angle (determines the starting point of the motion).
A pendulum is a classic example of Simple Harmonic Motion, as it swings back and forth under the influence of gravity. The restoring force is provided by the tension in the string, and the motion is periodic and follows the same equation as SHM.
Some real-world examples of Simple Harmonic Motion include the motion of a mass on a spring, the vibration of guitar strings, and the swinging of a pendulum. SHM can also be seen in the oscillations of sound waves and electromagnetic waves.