Simple Harmonic Motion Explained: IB Physics Revision Guide

Simple harmonic motion is one of those IB Physics topics that looks friendly until the graph, equation and direction of force all appear in the same question.

The safest route is to keep one idea at the centre: in simple harmonic motion, the acceleration is proportional to displacement from equilibrium and directed back toward equilibrium.

Quick Answer

• Simple harmonic motion is oscillation where acceleration is proportional to displacement and opposite in direction.
• The key relationship is a proportional to -x.
• The restoring force always acts toward the equilibrium position.
• Amplitude is the maximum displacement from equilibrium, not the full peak-to-peak distance.
• Period is the time for one complete oscillation.
• Frequency is the number of oscillations per second.
• Use f = 1 / T and T = 1 / f carefully.

What Makes Motion Simple Harmonic

For motion to be simple harmonic, the object must experience a restoring acceleration directed toward equilibrium. The further it is displaced, the larger the acceleration back toward equilibrium.

In exam language:

The acceleration is directly proportional to displacement from equilibrium and acts in the opposite direction.

That single sentence is often the definition the markscheme wants. If you only write "it moves back and forth", you have described oscillation, not simple harmonic motion.

Restoring Force and Equilibrium

The equilibrium position is where the resultant force is zero. When the object is displaced from that position, a restoring force acts to return it.

For a spring system, this links to Hooke's law:

The direction is the exam trap. If the object is displaced to the right, the restoring force is to the left. If the object is displaced upward, the restoring force is downward.

How to Read an SHM Graph

A displacement-time graph for SHM is sinusoidal. You do not need to panic when you see the curve. Start by labelling amplitude and period.

Use the graph to read values before reaching for equations. Many mistakes happen because students plug in the wrong time interval as the period.

Period, Frequency and Units

Period and frequency are linked by:

The units help you catch mistakes. Period is measured in seconds. Frequency is measured in hertz, which means per second.

If a question says an oscillator completes 5 oscillations in 20 seconds, the period is 20 / 5 = 4 seconds. The frequency is 5 / 20 = 0.25 Hz.

Worked Example

Question: A mass on a spring oscillates with a period of 0.80 s. Find its frequency.

Answer: Use f = 1 / T.

f = 1 / 0.80 = 1.25 Hz

Why this works: The period is the time for one oscillation, so the frequency is the reciprocal.

Common Exam Mistakes

These are the mistakes to remove before your exam:

One clean sketch usually prevents half of these errors.

How EduNinja Helps with SHM

Use IB Physics simple harmonic motion questions to practise definitions, graph reading and period-frequency calculations. If you need the related wave language, use the IB Physics wave model questions after this topic.

For a broader mixed set, open the IB Physics SL Question Bank and practise short-response questions where direction, units and graph reading matter.

Related Study Links

• IB Physics simple harmonic motion questions
• IB Physics wave model questions
• IB Physics standing waves and resonance questions
• IB Physics SL Question Bank
• IB Physics Question Bank

FAQ

What is simple harmonic motion in IB Physics?

Simple harmonic motion is oscillation where acceleration is directly proportional to displacement from equilibrium and directed toward equilibrium. In short, the acceleration acts opposite to displacement.

Is amplitude the same as peak-to-peak distance?

No. Amplitude is the maximum displacement from equilibrium. Peak-to-peak distance is twice the amplitude, from the highest point to the lowest point on a displacement graph.

Where is speed maximum in simple harmonic motion?

Speed is maximum at the equilibrium position. At that point, displacement is zero, but the object is moving fastest as it passes through the centre of the oscillation.

Where is acceleration maximum in simple harmonic motion?

Acceleration is maximum at maximum displacement, where the restoring force is largest. At equilibrium, acceleration is zero because displacement from equilibrium is zero.

Final Takeaway

Use this memory line: force back, acceleration back, amplitude from the middle. If you can keep direction and graph labels clean, SHM questions become much less slippery.