3.1.2

Simple Harmonic Motion

Test yourself on Simple Harmonic Motion

Test your knowledge with free interactive questions on Seneca — used by over 10 million students.

Simple Harmonic Motion (SHM)

SHM is any motion in which the acceleration is directed towards a fixed point (or equilibrium position for 1-D examples) AND is directly proportional to the negative of the displacement.

Formulae

Formulae

Mathematically, the definition of SHM can be expressed in a formula:
- $a=-\omega^2 x$
  - a is the acceleration.
  - $\omega = 2\pi f$ , where f is the frequency of oscillation
  - x is the displacement.

Acceleration-displacement graph

Acceleration-displacement graph

The acceleration-displacement graph is a straight-line graph that passes through the origin.
The angular frequency can be found from the gradient:
- gradient $= -\omega^2$
- $\omega = \sqrt{-gradient}$

Calculating maximum acceleration

Calculating maximum acceleration

If we are given the time period, T (or the frequency f), ω² can be calculated.
The maximum acceleration is given by:
- $a_{max}=\omega^2A$
  - where A is the maximum displacement.

Simple Harmonic Motion (SHM) Graphs

SHM can be represented graphically.

Acceleration and displacement

Acceleration and displacement

The acceleration can be found graphically, and so the displacement or vice versa from a graph.
- E.g. if you have a displacement-time graph, you can calculate the period and angular frequency.
The displacement at any point can be read off the graph. This means you can calculate the acceleration (and then even the net force) because $a=-\omega^2 x$ .

Velocity and displacement

Velocity and displacement

The velocity at any given time is found from the gradient of a displacement-time graph.
By finding the gradient at each point in time, we can produce a velocity-time graph from a displacement-time graph.

Velocity and acceleration

Velocity and acceleration

In a similar way, you can use a velocity-time graph to get the corresponding acceleration-time graph. This is because the gradient at a point on any velocity-time graph gives the acceleration at that moment in time.
You can then see that the acceleration-time graph is exactly the same shape as the displacement-time graph, reflected in the x-axis.

Simple Harmonic Equations

The condition for simple harmonic motion is that the acceleration is directed towards a fixed point and that the magnitude of the acceleration is proportional to the negative of the displacement.

Oscillations

Oscillations

For SHM the acceleration must be proportional to the negative of the displacement. $a{\alpha}-x$
If an object is under SHM it's displacement is found by $x=A\cos({\omega}t)$ where A is the amplitude
The defining equation of SHM is $a=-{\omega}^2x$

Maximum points

The maximum displacement can be found when $\cos({\omega}t)=1$
The maximum displacement is called the amplitude A
The maximum speed is given by $v={\omega}A$
The maximum acceleration is given by $a={\omega}^2A$

1

Space, Time & Motion

1.1

Motion

1.1.1Motion Basics 1.1.2Graphs of Motion 1.1.3Uniform Acceleration Equations 1.1.4Projectile Motion 1.1.5Bouncing Ball Example

1.2

Forces

1.2.1Friction 1.2.2Terminal Speed 1.2.3Newton's Laws 1.2.4Exam-Style Question - Forces 1.2.5End of Topic Test - Newton's Third Law

1.3

Momentum & Impulse

1.3.1Momentum 1.3.2Momentum 2 1.3.3End of Topic Test - Newton's Laws & Momentum

1.4

Work, Energy & Power

1.4.1Work & Energy 1.4.2Conservation of Energy 1.4.3Power & Efficiency 1.4.4IB Multiple Choice- Work, Energy & Power

2

The Particulate Nature of Matter

2.1

Thermal Concepts

2.1.1Molecular Kinetic Theory Model 2.1.2Molecular Kinetic Theory Model 2 2.1.3Thermal Energy Transfer 2.1.4Thermal Energy Transfer Experiments 2.1.5Thermal Equilibrium 2.1.6Thermal Conductivity 2.1.7Heat Energy Transfer

2.2

Modelling a Gas

2.2.1Ideal Gases 2.2.2Ideal Gases 2 2.2.3End of Topic Test - Thermal Energy & Ideal Gases 2.2.4Exam-Style Question - Ideal Gases

3

Wave Behaviour

3.1

Oscillations

3.1.1Progressive Waves 3.1.2Simple Harmonic Motion

3.2

Travelling Waves

3.2.1Wave Speed & Phase Difference 3.2.2Longitudinal & Transverse Waves 3.2.3Electromagnetic Waves 3.2.4Electromagnetic Waves 2 3.2.5Sound Waves

3.3

Wave Characteristics

3.3.1Polarisation

3.4

Wave Behaviour

3.4.1Reflection & Absorption 3.4.2Reflection of Light 3.4.3Refraction 3.4.4Refractive index

3.5

Standing Waves

3.5.1Standing Waves 3.5.2Standing Waves 2 3.5.3End of Topic Test - Standing Waves 3.5.4IB Multiple Choice - Waves

3.6

Simple Harmonic Motion

3.6.1Simple Harmonic Motion 3.6.2Simple Harmonic Systems 3.6.3Energy in Simple Harmonic Motion 3.6.4End of Topic Test - Simple Harmonic Motion 3.6.5End of Topic Test - Simple Harmonic Motion

3.7

Single Slit Diffraction

3.7.1Diffraction

3.8

Interference

3.8.1Interference 3.8.2Interference 2 3.8.3Diffraction Gratings 3.8.4End of Topic Test - Diffraction

3.9

Doppler Effect

3.9.1Doppler Effect

4

Fields

4.1

Circular Motion

4.1.1Circular Motion 4.1.2Centripetal Force 4.1.3IB Multiple Choice - Circular Motion

4.2

Newton's Law of Gravitation

4.2.1Newton's Law 4.2.2Orbits of Planets & Satellites 4.2.3Escape Velocity & Synchronous Orbits 4.2.4End of Topic Test - Gravitational Fields

4.3

Fields

4.3.1Fields 4.3.2Gravitational Field Strength 4.3.3Gravitational Potential 4.3.4Electric Field Strength 4.3.5Electrostatic & Gravitational Forces 4.3.6Electric Potential 4.3.7IB Multiple Choice - Gravitational Fields

4.4

Fields at Work

4.4.1Radial Field Strength 4.4.2Orbits of Planets & Satellites 4.4.3Escape Velocity & Synchronous Orbits 4.4.4End of Topic Test - Gravitational Fields 4.4.5Uniform Electric Fields 4.4.6IB Multiple Choice - Electric Field & Potential

4.5

Electric Fields

4.5.1Electric Charge 4.5.2Conservation of Charge 4.5.3Coulomb's Law 4.5.4Current 4.5.5Potential Difference 4.5.6IB Multiple Choice - Electric Charge

4.6

Magnetic Effect of Electric Currents

4.6.1Magnetism 4.6.2Magnetic Field 4.6.3Magnetic Force 4.6.4Moving Charges in a Magnetic Field 4.6.5IB Multiple Choice - Magnetism

4.7

Heating Effect of Currents

4.7.1Circuits 4.7.2Resistance 4.7.3Power and Conservation 4.7.4IB Multiple Choice - DC Circuits

4.8

Electromagnetic Induction

4.8.1Electromagnetic Induction 4.8.2Electromagnetic Induction 2 4.8.3Magnetic Flux & Flux Linkage 4.8.4End of Topic Test - Electromagnetic Induction

4.9

Power Generation & Transmission

4.9.1Alternating Currents 4.9.2Operation of a Transformer

4.10

Capacitance

4.10.1Capacitance 4.10.2Parallel Plate Capacitor 4.10.3Energy Stored by a Capacitor 4.10.4Capacitor Discharge 4.10.5Capacitor Charge 4.10.6Magnetic Flux Density 4.10.7End of Topic Test - Capacitance & Flux Density

5

Nuclear & Quantum Physics

5.1

Discrete Energy & Radioactivity

5.1.1Atomic Spectra 5.1.2Atomic Structure 5.1.3Photons 5.1.4Discrete Energy Levels 5.1.5Alpha, Beta & Gamma Radiation 5.1.6Scientific Practices - Unstable Nuclei 5.1.7Radioactive Decay 5.1.8IB Multiple Choice - Atomic Physics

5.2

Nuclear Reactions

5.2.1Mass & Energy 5.2.2Nuclear Fission

5.3

The Interaction of Matter with Radiation

5.3.1Particles, Antiparticles & Photons 5.3.2Particle Interactions 5.3.3Classification of Particles 5.3.4Wave-Particle Duality 5.3.5Wave Functions & Probability 5.3.6IB Multiple Choice - Quantum Physics

5.4

Nuclear Physics

5.4.1Nuclear Instability & Radioactive Decay 5.4.2Nuclear Radius 5.4.3IB Multiple Choice - Nuclear Physics

6

Measurements

6.1

Measurements & Errors

6.1.1Fundamental Units 6.1.2SI Prefixes, Standard Form & Converting Units 6.1.3End of Topic Test - Units & Prefixes

6.2

Uncertainties & Errors

6.2.1Limitation of Physical Measurements 6.2.2Uncertainty 6.2.3Estimation 6.2.4End of Topic Test - Measurements & Errors

6.3

Vectors & Scalars

6.3.1Scalars & Vectors 6.3.2Vector Problems

Jump to other topics

1

Space, Time & Motion

1.1

Motion

1.1.1Motion Basics 1.1.2Graphs of Motion 1.1.3Uniform Acceleration Equations 1.1.4Projectile Motion 1.1.5Bouncing Ball Example

1.2

Forces

1.2.1Friction 1.2.2Terminal Speed 1.2.3Newton's Laws 1.2.4Exam-Style Question - Forces 1.2.5End of Topic Test - Newton's Third Law

1.3

Momentum & Impulse

1.3.1Momentum 1.3.2Momentum 2 1.3.3End of Topic Test - Newton's Laws & Momentum

1.4

Work, Energy & Power

1.4.1Work & Energy 1.4.2Conservation of Energy 1.4.3Power & Efficiency 1.4.4IB Multiple Choice- Work, Energy & Power

2

The Particulate Nature of Matter

2.1

Thermal Concepts

2.1.1Molecular Kinetic Theory Model 2.1.2Molecular Kinetic Theory Model 2 2.1.3Thermal Energy Transfer 2.1.4Thermal Energy Transfer Experiments 2.1.5Thermal Equilibrium 2.1.6Thermal Conductivity 2.1.7Heat Energy Transfer

2.2

Modelling a Gas

2.2.1Ideal Gases 2.2.2Ideal Gases 2 2.2.3End of Topic Test - Thermal Energy & Ideal Gases 2.2.4Exam-Style Question - Ideal Gases

3

Wave Behaviour

3.1

Oscillations

3.1.1Progressive Waves 3.1.2Simple Harmonic Motion

3.2

Travelling Waves

3.2.1Wave Speed & Phase Difference 3.2.2Longitudinal & Transverse Waves 3.2.3Electromagnetic Waves 3.2.4Electromagnetic Waves 2 3.2.5Sound Waves

3.3

Wave Characteristics

3.3.1Polarisation

3.4

Wave Behaviour

3.4.1Reflection & Absorption 3.4.2Reflection of Light 3.4.3Refraction 3.4.4Refractive index

3.5

Standing Waves

3.5.1Standing Waves 3.5.2Standing Waves 2 3.5.3End of Topic Test - Standing Waves 3.5.4IB Multiple Choice - Waves

3.6

Simple Harmonic Motion

3.6.1Simple Harmonic Motion 3.6.2Simple Harmonic Systems 3.6.3Energy in Simple Harmonic Motion 3.6.4End of Topic Test - Simple Harmonic Motion 3.6.5End of Topic Test - Simple Harmonic Motion

3.7

Single Slit Diffraction

3.7.1Diffraction

3.8

Interference

3.8.1Interference 3.8.2Interference 2 3.8.3Diffraction Gratings 3.8.4End of Topic Test - Diffraction

3.9

Doppler Effect

3.9.1Doppler Effect

4

Fields

4.1

Circular Motion

4.1.1Circular Motion 4.1.2Centripetal Force 4.1.3IB Multiple Choice - Circular Motion

4.2

Newton's Law of Gravitation

4.2.1Newton's Law 4.2.2Orbits of Planets & Satellites 4.2.3Escape Velocity & Synchronous Orbits 4.2.4End of Topic Test - Gravitational Fields

4.3

Fields

4.3.1Fields 4.3.2Gravitational Field Strength 4.3.3Gravitational Potential 4.3.4Electric Field Strength 4.3.5Electrostatic & Gravitational Forces 4.3.6Electric Potential 4.3.7IB Multiple Choice - Gravitational Fields

4.4

Fields at Work

4.4.1Radial Field Strength 4.4.2Orbits of Planets & Satellites 4.4.3Escape Velocity & Synchronous Orbits 4.4.4End of Topic Test - Gravitational Fields 4.4.5Uniform Electric Fields 4.4.6IB Multiple Choice - Electric Field & Potential

4.5

Electric Fields

4.5.1Electric Charge 4.5.2Conservation of Charge 4.5.3Coulomb's Law 4.5.4Current 4.5.5Potential Difference 4.5.6IB Multiple Choice - Electric Charge

4.6

Magnetic Effect of Electric Currents

4.6.1Magnetism 4.6.2Magnetic Field 4.6.3Magnetic Force 4.6.4Moving Charges in a Magnetic Field 4.6.5IB Multiple Choice - Magnetism

4.7

Heating Effect of Currents

4.7.1Circuits 4.7.2Resistance 4.7.3Power and Conservation 4.7.4IB Multiple Choice - DC Circuits

4.8

Electromagnetic Induction

4.8.1Electromagnetic Induction 4.8.2Electromagnetic Induction 2 4.8.3Magnetic Flux & Flux Linkage 4.8.4End of Topic Test - Electromagnetic Induction

4.9

Power Generation & Transmission

4.9.1Alternating Currents 4.9.2Operation of a Transformer

4.10

Capacitance

4.10.1Capacitance 4.10.2Parallel Plate Capacitor 4.10.3Energy Stored by a Capacitor 4.10.4Capacitor Discharge 4.10.5Capacitor Charge 4.10.6Magnetic Flux Density 4.10.7End of Topic Test - Capacitance & Flux Density

5

Nuclear & Quantum Physics

5.1

Discrete Energy & Radioactivity

5.1.1Atomic Spectra 5.1.2Atomic Structure 5.1.3Photons 5.1.4Discrete Energy Levels 5.1.5Alpha, Beta & Gamma Radiation 5.1.6Scientific Practices - Unstable Nuclei 5.1.7Radioactive Decay 5.1.8IB Multiple Choice - Atomic Physics

5.2

Nuclear Reactions

5.2.1Mass & Energy 5.2.2Nuclear Fission

5.3

The Interaction of Matter with Radiation

5.3.1Particles, Antiparticles & Photons 5.3.2Particle Interactions 5.3.3Classification of Particles 5.3.4Wave-Particle Duality 5.3.5Wave Functions & Probability 5.3.6IB Multiple Choice - Quantum Physics

5.4

Nuclear Physics

5.4.1Nuclear Instability & Radioactive Decay 5.4.2Nuclear Radius 5.4.3IB Multiple Choice - Nuclear Physics

6

Measurements

6.1

Measurements & Errors

6.1.1Fundamental Units 6.1.2SI Prefixes, Standard Form & Converting Units 6.1.3End of Topic Test - Units & Prefixes

6.2

Uncertainties & Errors

6.2.1Limitation of Physical Measurements 6.2.2Uncertainty 6.2.3Estimation 6.2.4End of Topic Test - Measurements & Errors

6.3

Vectors & Scalars

6.3.1Scalars & Vectors 6.3.2Vector Problems

Practice questions on Simple Harmonic Motion

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

1
Which statements about simple harmonic motion are true?True / false
2
What is the correct equation for the maximum acceleration? Multiple choice
3
What can be found using the gradient of an acceleration-displacement graph?Multiple choice
4
Which statements about SHM graphs are true?True / false
5
How do an acceleration-time and a displacement-time graph differ in simple harmonic motion?Multiple choice

Answer all questions on Simple Harmonic Motion

Unlock your full potential with Seneca Premium

Unlimited access to 10,000+ open-ended exam questions
Mini-mock exams based on your study history
Unlock 800+ premium courses & e-books

Get started with Seneca Premium

Progressive Waves

Wave Speed & Phase Difference