A particle is said to have $$SHM$$ if the acceleration of the particle
is directly proportional to its displacement from the mean position and
directed towards the mean position.
E.g. :
1- Vertical oscillations of a loaded spring.
2- Oscillation of bob of a simple pendulum.
3- vibration of string of musical instruments.
4- Motion of air particles during the propagation of sound waves.
5- Vibration of tuning fork.