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Theme C — Wave Behaviour

C.1 Simple Harmonic Motion — IB Physics SL Revision Notes & Topical Questions

5 min read 10 parts Lesson 2 of 31 1 quiz

📚 IB Physics SL Hub / Topical Revision
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Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

C.1 Simple Harmonic Motion — IB PHYSICS SL notes: Describe the conditions for simple harmonic motion and analyse a mass–spring system and a simple pendulum, including energy changes.Displacement — x is measured from the equilibrium positionAmplitude — x0 is the maximum displaceme…

  • Frequency and angular frequency
  • What the symbols mean
  • Restoring force
  • Minus sign
  • Equation of motion
  • Effect of changes

Section 1 of 10Describing oscillations

1Displacement
  • Displacement x is measured from the equilibrium position
2Amplitude
  • Amplitude x0 is the maximum displacement
3Period
  • T is the time for one full cycle
4Frequency and angular frequency
  • Frequency and angular frequency f = 1/T and ω = 2πf = 2π/T

Section 2 of 10Condition for SHM

Simple harmonic motion
  • Simple harmonic motion oscillation in which the acceleration is proportional to displacement from equilibrium and directed towards it
  • a = −ω2x
    What the symbols mean: a = acceleration (m s−2) · ω = angular frequency (rad s−1) · x = displacement from equilibrium (m); the minus sign means a always points back to the centre
Restoring force
  • Restoring force a force proportional to displacement and always directed towards equilibrium gives SHM
Minus sign
  • Minus sign the acceleration is always directed towards equilibrium
a–x graph
  • a–x graph a straight line through the origin with gradient −ω2
Period
  • Period it is independent of amplitude

Section 3 of 10Mass–spring system

Mass–spring system
Equation of motion
  • F = −kx gives ω2 = k/m
Period
  • T = 2π√(m/k)
    What the symbols mean: T = period (s) · m = mass on the spring (kg) · k = spring constant (N m−1)
Effect of changes
  • Effect of changes a stiffer spring shortens the period and a larger mass lengthens it
Gravity
  • Gravity it does not affect the period of a vertical spring

Section 4 of 10Simple pendulum

Period
  • T = 2π√(l/g) for small angles, below about 10°
Independence
  • Independence the period does not depend on mass or amplitude

Section 5 of 10Graphs of SHM

Same period
  • Same period x, v and a all vary sinusoidally with the same period
Velocity
  • Velocity it is the gradient of the x–t graph and is a quarter of a cycle ahead of the displacement
Acceleration
  • Acceleration it is in antiphase with the displacement

Section 6 of 10Energy in SHM

At maximum displacement
  • At maximum displacement kinetic energy is zero and potential energy is maximum
At equilibrium
  • At equilibrium kinetic energy is maximum and potential energy is minimum
Total energy
  • Total energy it is constant without damping and proportional to amplitude squared

Section 7 of 10One cycle step by step

1
At +x0 the speed is zero, the acceleration is maximum towards the centre and all the energy is potential.
2
Moving to the centre, the speed rises and the acceleration falls.
3
At the centre the speed is maximum, the acceleration is zero and all the energy is kinetic.
4
Moving to −x0, the speed falls and the acceleration grows in the opposite sense.
5
The motion reverses and the cycle repeats after time T.

Section 8 of 10Mass–spring and pendulum compared

FeatureMass–springSimple pendulum
Period2π√(m/k)2π√(l/g)
Depends on mass?YesNo
Depends on g?NoYes
Restoring forceSpring forceComponent of weight

Section 9 of 10Key terms

TermMeaning
Simple harmonic motionOscillation in which acceleration is proportional to displacement from equilibrium and directed towards the equilibrium position.
AmplitudeThe maximum displacement from the equilibrium position.
PeriodThe time for one complete oscillation.
FrequencyThe number of oscillations per unit time.
Angular frequencyω = 2πf = 2π/T.
Restoring forceA force that always acts towards the equilibrium position.

Section 10 of 10Exam technique

Avoid these mistakes
Saying the period of a pendulum depends on its mass — it depends only on length and g.
Believing the acceleration is maximum at equilibrium — it is zero there and maximum at the extremes.
Using the pendulum formula for large angles — it holds only for small angles.

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