C.1
Simple Harmonic Motion
SHM definitions, the defining equation, energy, graphs and examples including pendulums and springs. HL extends to phase angle and algebraic energy methods.
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C.1 Simple Harmonic Motion
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C.1 Simple Harmonic Motion — SL
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Key Concepts, Simple Harmonic Motion
The Two Conditions for SHM
Simple Harmonic Motion requires two conditions to be satisfied. First, the restoring force must always act towards the equilibrium position. Second, the magnitude of the restoring force must be directly proportional to the displacement from equilibrium. Together, these conditions produce the defining equation a = -ω²x, where the negative sign is crucial: it tells you the acceleration always points in the opposite direction to the displacement, pulling the object back towards the centre. If either condition fails, the motion is oscillatory but not SHM.
Defining Quantities in SHM
The key quantities are: amplitude A (the maximum displacement from equilibrium, in metres), time period T (the time for one complete oscillation, in seconds), frequency f (the number of complete oscillations per second, in hertz, where f = 1/T), and angular frequency ω (defined as ω = 2πf, in rad/s). The equilibrium position is where the net force is zero and the object would rest if undisturbed. Displacement x is measured from this point and can be positive or negative. Amplitude is always positive.
Time Period for Springs and Pendulums
For a mass m on a spring with spring constant k, the time period is T = 2π√(m/k). Note that T increases with mass (heavier objects oscillate more slowly) and decreases with spring constant (stiffer springs produce faster oscillations). For a simple pendulum of length L in a gravitational field of strength g, the time period is T = 2π√(L/g). This assumes small oscillations (less than about 10°). Critically, the pendulum period does not depend on mass or amplitude, only on length and g.
Energy in SHM
During SHM, energy continuously converts between kinetic energy (KE) and potential energy (PE). At maximum displacement (amplitude), velocity is zero so KE = 0 and PE is maximum. At the equilibrium position, displacement is zero, velocity is maximum, so KE is maximum and PE = 0. The total mechanical energy E = ½mω²A² remains constant throughout (assuming no damping). On an energy-displacement graph, KE appears as an inverted parabola and PE as an upright parabola; they always add to the same total.
SHM Graphs
The displacement-time graph for SHM is a sine or cosine curve depending on starting conditions. The velocity-time graph is also sinusoidal, but 90° ahead in phase (velocity is maximum when displacement is zero and zero when displacement is maximum). The acceleration-time graph is a reflected version of the displacement-time graph (180° out of phase): when displacement is maximum positive, acceleration is maximum negative. The acceleration-displacement graph is a straight line with negative gradient through the origin, with gradient equal to -ω². This graph is the most direct way to verify SHM.
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Frequently Asked Questions, IB Physics Simple Harmonic Motion
What is Simple Harmonic Motion in IB Physics? ↓
SHM definitions, the defining equation, energy, graphs and examples including pendulums and springs. HL extends to phase angle and algebraic energy methods. This topic is part of Theme C (Wave Behaviour) in the current IB Physics syllabus.
Is Simple Harmonic Motion SL or HL in IB Physics? ↓
Simple Harmonic Motion is covered by both SL and HL students in the current IB Physics syllabus. HL students study additional depth and extension content beyond the SL core.
What equations do I need for IB Physics Simple Harmonic Motion? ↓
The key equations for Simple Harmonic Motion are covered in the concept tutorial above. For a structured set of notes with all equations, conditions and worked examples, the GradePod Exam Pack includes a revision note template for every topic.
What are common exam mistakes in IB Physics Simple Harmonic Motion? ↓
Common mistakes are covered in detail in the exam technique video above. The GradePod Exam Pack also includes exam-style questions with mark schemes so you can see exactly how marks are awarded and where students typically drop them.
How do I revise Simple Harmonic Motion for the IB Physics exam? ↓
Follow the GradePod three-step method. First, watch the concept tutorial and tick off each learning objective on the checklist above as you go. Second, watch the exam technique video to see how IB-style questions are answered under exam conditions. Third, use the Exam Pack to practise independently with knowledge questions, exam questions and mark schemes. That's it. It works. I promise.