The displacement of a particle executing simple harmonic motion is given by y=A₀+A sin ω t+B cos ω t. Then the amplitude of its oscillation is given by

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(3) √A²+B². Given: y=A₀+A sin ω t+B cos ω t. Idea: a constant shifts the centre of the motion; only the two sinusoids set the amplitude. Write A sin ω t+B cos ω t=R sin(ω t+φ). Expanding, R cos φ=A and R sin φ=B. R²=A²+B² y=A₀+R sin(ω t+φ), so the particle swings by ± R about y=A₀. Amplitude =√A²+B²

The displacement of a particle executing simple harmonic motion is given by y=A₀+A sin ω t+B cos ω t. Then the amplitude of its oscillation is given by

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