Observe the motion along this line.

## Summary/Background

- the distance OP is called the amplitude
- the velocity is greatest at O
- the velocity is zero at P and P'
- the acceleration is zero at O
- the acceleration is greatest at the end points P and P'.
- this motion is called simple harmonic motion
- the equation \ddot{x} = -\omega^2 x described the motion

## Software/Applets used on this page

Uses Cinderella interactive geometry

## Glossary

### acceleration

the rate of change of velocity with time. It is a vector quantity with magnitude and direction.

### amplitude

The maximum displacement from the x axis in either the positive or negative direction.

### equation

A statement that two mathematical expressions are equal.

### simple harmonic motion

the motion of a particle moving in a straight line whose acceleration is always towards a fixed point on the line and is proportional to its distance from that point

### velocity

the rate of change of displacement. It is a vector quantity with magnitude and direction.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

AQA A-Level (UK - Pre-2017) | M5 | Further Dynamics | SHM | - |

AQA A2 Further Maths 2017 | Pure Maths | Modelling with Differential Equations | Simple Harmonic Motion | - |

AQA AS/A2 Further Maths 2017 | Pure Maths | Modelling with Differential Equations | Simple Harmonic Motion | - |

CCEA A-Level (NI) | M3 | Further Dynamics | SHM | - |

Edexcel A-Level (UK - Pre-2017) | M3 | Further Dynamics | SHM | - |

Edexcel A2 Further Maths 2017 | Further Mechanics 2 | Dynamics | Simple Harmonic Motion | - |

Edexcel AS/A2 Further Maths 2017 | Further Mechanics 2 | Dynamics | Simple Harmonic Motion | - |

OCR A-Level (UK - Pre-2017) | M3 | Further Dynamics | SHM | - |

OCR A2 Further Maths 2017 | Pure Core | Modelling with Differential Equations | Simple Harmonic Motion | - |

OCR MEI A2 Further Maths 2017 | Core Pure B | Modelling with Differential Equations | Simple Harmonic Motion | - |

OCR-MEI A-Level (UK - Pre-2017) | M3 | Further Dynamics | SHM | - |

Universal (all site questions) | F | Further Dynamics | SHM | - |

WJEC A-Level (Wales) | M3 | Further Dynamics | SHM | - |