Flashcards · 9702 · A Level Topic 17

Oscillations (A Level) flashcards

17 cards on A Level Topic 17, subtopics 17.1 to 17.3. Pick a subtopic or study them all.

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Simple harmonic motion: Motion in which the acceleration is proportional to the displacement from a fixed point and always directed towards that point: a = −ω²x.
Angular frequency of an oscillation: ω = 2πf = 2π ÷ T. Unit rad s⁻¹.
When do you use x = x₀ sin ωt and when x = x₀ cos ωt?: x = x₀ sin ωt: timing starts at the equilibrium position. x = x₀ cos ωt: timing starts at maximum displacement.
Speed in SHM at displacement x, and the maximum speed: v = ±ω√(x₀² − x²). Maximum v₀ = ωx₀, at the equilibrium position (x = 0).
Amplitude 0.030 m, ω = 6.0 rad s⁻¹. Find the maximum acceleration.: a_max = ω²x₀ = 36 × 0.030 = 1.08 m s⁻², at maximum displacement.
Phase relationships between displacement, velocity and acceleration in SHM: Velocity is 90° (π/2) out of phase with displacement. Acceleration is 180° (π) out of phase with displacement.

Total energy of a simple harmonic oscillator: E = ½mω²x₀². It is constant (no damping).
Kinetic and potential energy at displacement x in SHM: Ek = ½mω²(x₀² − x²). Ep = ½mω²x². They add up to the constant total ½mω²x₀².
Describe the energy interchange in one cycle of SHM: At equilibrium the energy is all kinetic; at maximum displacement it is all potential. Energy transfers back and forth twice per cycle; the total stays constant.
A 0.20 kg mass oscillates with amplitude 0.050 m and ω = 4.0 rad s⁻¹. Find its total energy.: E = ½mω²x₀² = 0.5 × 0.20 × 4.0² × 0.050² = 4.0 × 10⁻³ J.
Shape of graphs of Ek and Ep against displacement in SHM: Both are parabolas (they vary with x²): Ep is zero at x = 0, Ek is zero at x = ±x₀, and their sum is a horizontal line.

Free, damped and forced oscillations: Free: at the natural frequency, with no external driving force (and ideally no energy loss). Damped: energy lost to resistive forces, so the amplitude falls. Forced: driven by an external periodic force at the driving frequency.
Light damping: The amplitude decays exponentially over many oscillations. The period is almost unchanged.
Critical damping: The system returns to equilibrium in the shortest time without oscillating. Used in car suspension.
Heavy (over) damping: The system returns to equilibrium slowly, without oscillating.
Resonance: When the driving frequency equals the natural frequency of the system, energy transfer is maximum and the amplitude of the forced oscillation is greatest.
How does increasing damping change a resonance curve?: The peak amplitude is lower, the peak moves to a slightly lower frequency, and the curve becomes broader (flatter).