Differential Equation Of Simple Harmonic Motion — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Differential Equation of Simple Harmonic Motion Valid for systems where the restoring force is directly proportional to the displacement and acts in the opposite direction (Hooke's Law). Start with Newton's Second Law: F = ma. Substitute the restoring force F = -kx. Substitute acceleration a = d²x/dt². Define ω² = k/m. Rearrange to obtain d²x/dt² + ω²x = 0. Motion must be one-dimensional or reducible to 1D. Small angle approximation required for simple pendulums. System must be frictionless/undamped for this specific form. Confusing angular frequency (ω) with frequency (f) or period (T). Believing acceleration is constant (it varies with displacement). Forgetting the negative sign implies the force is restorative (towards equilibrium).