Oscillations · revision map · A-Level 9702, Topic 17

TOPIC 17 · OSCILLATIONS
CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS 9702 · ONE-PAGE REVISION MAP
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OSCILLATIONS17 · SHM
Defining SHM

Acceleration points back to equilibrium and is set by the displacement: a ∝ x, but always opposite to x.

a = −ω² x
the defining
equation of SHM
  • Amplitude x0, period T, frequency f.
  • Angular frequency ω = 2πf = 2π/T.
  • Phase difference φ compares two oscillators, in radians.
+x a equilibrium a points back to centre
Solutions & Graphs

Sinusoids in time: displacement and velocity a quarter cycle out of step.

x = x0 cos ωt
(or x0 sin ωt)
v = ±ω√(x0² − x²)
  • Speed is greatest at x = 0; vmax = ωx0.
  • v = 0 at the turning points x = ±x0.
x v t v (dashed) leads x by a quarter period
Energy in SHM

Kinetic and potential energy trade, but if undamped the total stays constant.

  • KE is greatest at the centre; PE is greatest at ±x0.
  • KE = ½mω²(x0² − x²), PE = ½mω²x².
  • Total energy ∝ amplitude squared.
E = ½ m ω² x0²
E PE KE 0 −x0 +x0
Damping & Resonance

Resistive forces drain energy; a driving force can feed it back.

  • Damping removes energy, so amplitude decays.
  • Light: many shrinking swings. Critical: fastest return, no overshoot. Heavy: slow creep, no oscillation.
  • Forced oscillation: a periodic driver sets the motion.
  • Resonance: driving at the natural f0 gives maximum amplitude; more damping lowers and broadens the peak.
light damping decay resonance peak f
BUILDS ON · Kinematics · Circular motion → OSCILLATIONS → LEADS TO · Alternating currents · Magnetic fields
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