C.1 Simple harmonic motionIB Physics HL: Flashcards

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Defining equation of SHM?

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Defining equation of SHM?: a = −ω²x.
Link between T, f and ω?: T = 1/f = 2π/ω.
Period of a mass–spring system and of a pendulum?: T = 2π√(m/k); T = 2π√(l/g) (small angles).
Where is speed greatest in SHM?: At equilibrium: v_max = ωx₀.
Where is acceleration greatest?: At the extremes: a_max = ω²x₀.
HL: What is phase angle?: The angle ϕ in x = x₀ sin(ωt + ϕ) describing the oscillator's state at t = 0.
HL: Phase difference from a time difference?: Δϕ = 2πΔt/T.
HL: ϕ if the oscillator starts at +x₀ (sine form)?: ϕ = π/2.
HL: Velocity equation in SHM?: v = ωx₀ cos(ωt + ϕ).
HL: Speed at displacement x?: v = ±ω√(x₀² − x²).
HL: Total energy of an SHM oscillator?: E_T = ½mω²x₀².
HL: Potential energy at displacement x?: E_P = ½mω²x².
HL: Where are kinetic and potential energy equal?: At x = ±x₀/√2.
HL: Effect of doubling amplitude on total energy?: Energy quadruples (E_T ∝ x₀²).