Simple harmonic motion (SHM) is a specific type of periodic motion characterized by a restoring force that is directly proportional to the displacement from an equilibrium position.

In SHM, an object oscillates back and forth around its equilibrium position. The term “simple” refers to the linear relationship between the restoring force and the displacement: the restoring force is strongest when the displacement is at its maximum and diminishes to zero as the object returns to the equilibrium position. The motion is described as “harmonic” because it follows a sinusoidal pattern, whereby the displacement, velocity, and acceleration all exhibit sinusoidal variations over time.

Several key parameters characterize simple harmonic motion:

• Amplitude ($A$): This is the maximum displacement from the equilibrium position.
• Period ($T$): The period is the time required for one complete oscillation.
• Frequency ($f$): This is the number of oscillations that occur in a unit of time and is the reciprocal of the period, given by the formula:

• Angular Frequency ($\omega$): This measures how quickly the object oscillates in radians per unit time and is related to frequency by the equation:

Simple harmonic motion is prevalent in various physical systems, including springs, pendulums, and waves. It is a fundamental concept in both physics and engineering and plays a crucial role in the design and analysis of many mechanical and electrical systems. A solid understanding of simple harmonic motion is essential for physics students, as it lays the groundwork for exploring more complex dynamical systems.