Simple harmonic motion
Oscillatory motion in which the acceleration is directly proportional to displacement but opposite in direction: a = −ω²x. The object undergoes periodic motion between extreme positions (amplitude A). Displacement varies sinusoidally: x = A sin(ωt + φ), where φ is the phase constant. Period T = 2π/ω is independent of amplitude.
Formula
a = −ω²x ; x = A sin(ωt + φ) ; T = 2π/ω
Real World
The pendulum inside a Foucault pendulum display at the Science Museum in London undergoes SHM; its 67-second period depends only on the cable length, not on how hard it was pushed.
Exam Focus
To show a system exhibits SHM, prove that acceleration is proportional to displacement and directed toward equilibrium — state both conditions explicitly.
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