Simple Harmonic Motion (SHM) is a type of periodic motion in which a particle oscillates back and forth around a stable equilibrium position. It is characterized by a restoring force that is directly proportional to the displacement of the particle from its equilibrium position and acts towards the equilibrium position.

Among the given options, the wave moving through a string fixed at both ends is an example of simple harmonic motion. Let's understand why.

- Simple Harmonic Motion (SHM): The motion of a wave can be described as a simple harmonic motion when it meets the conditions of SHM. In SHM, the motion is periodic, and the restoring force is proportional to the displacement from the equilibrium position.

- Wave Moving Through a String: When a wave travels through a string fixed at both ends, it exhibits simple harmonic motion. Here's why:

1. Restoring Force: In a wave moving through a string, the tension in the string provides the restoring force. When the string is displaced from its equilibrium position, it experiences a tension force that acts to restore it back to equilibrium. This restoring force is directly proportional to the displacement and acts opposite to the displacement.

2. Periodic Motion: As the wave moves along the string, it undergoes repeated oscillations back and forth. Each point on the string experiences simple harmonic motion as it oscillates around its equilibrium position. The motion is periodic, with a constant frequency determined by the wave source.

3. Displacement and Restoring Force Relationship: The displacement of a point on the string from its equilibrium position determines the magnitude of the restoring force. The further the point is displaced, the greater the restoring force trying to bring it back to equilibrium. This relationship follows Hooke's Law, which is a characteristic of simple harmonic motion.

Therefore, a wave moving through a string fixed at both ends is an example of simple harmonic motion. The restoring force provided by the tension in the string is directly proportional to the displacement, and the motion is periodic and repetitive. This type of motion is commonly observed in various wave phenomena, such as water waves, sound waves, and electromagnetic waves.