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Simple Harmonic Motion is the foundational oscillatory motion in physics, defined by the condition that acceleration is proportional to displacement and directed toward the equilibrium position: $a = -\omega^2 x$. This arises whenever a restoring force obeys Hooke's law $F = -kx$. The motion is completely described by three parameters: amplitude $A$, angular frequency $\omega = \sqrt{k/m}$, and initial phase $\phi$.

The displacement follows $x = A\sin(\omega t + \phi)$, with velocity $v = A\omega\cos(\omega t + \phi)$ and acceleration $a = -A\omega^2\sin(\omega t + \phi)$. The time period $T = 2\pi/\omega$ is independent of amplitude — a hallmark of SHM that distinguishes it from general oscillatory motion. Two canonical systems dominate JEE problems: the spring-mass system ($T = 2\pi\sqrt{m/k}$, gravity-independent) and the simple pendulum ($T = 2\pi\sqrt{l/g}$, mass-independent). Understanding SHM is essential because it appears across mechanics (springs, pendulums), waves (standing waves), electromagnetism (LC circuits), and even modern physics (vibrating atoms). The mathematical framework — sinusoidal functions, phase relationships, and energy conservation — forms the backbone of wave physics.