This applet shows the two dimensional spring pendulum: a mass suspended on a spring. The pendulum moves under the influence of gravity and the elastic force of the spring. The apparently simple motion of this system is complex enough that no equations exist that would describe its path. The motion of the system is calculated using Newton's Second Law: a = Fnet / M.
The net force is the vector sum of the gravitational force Mg and the elastic force of the spring F = - k x.
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Glossary
elastic
of a spring or string that changes in length when a force is applied
force
that which causes a body to accelerate or change in momentum
gravity
the force that the Earth exerts on all objects. It acts towards the centre of the Earth.
If the mass of the object is m kg then this force is defined to be mg Newtons, where g is the acceleration due to gravity.
If the mass of the object is m kg then this force is defined to be mg Newtons, where g is the acceleration due to gravity.
mass
a measure of the quantity of matter in an object
newton's second law
the force applied to a particle is proportional to the mass of the particle and the acceleration produced: F = ma
path
A finite sequence of edges such that the end vertex of one edge in the sequence is the start vertex of the next and in which no vertex appears more than once.
pendulum
a body that oscillates about a fixed axis under gravity
spring
a helical wire or string made of rubber which when stretched and let go returns to its original shape
vector
A mathematical object 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 | Elastic springs and strings | - |
| AQA AS Further Maths 2017 | Mechanics | Work, Energy and Power | Elastic Springs and Strings | - |
| AQA AS/A2 Further Maths 2017 | Mechanics | Work, Energy and Power | Elastic Springs and Strings | - |
| CCEA A-Level (NI) | M3 | Further Dynamics | Elastic springs and strings | - |
| Edexcel A-Level (UK - Pre-2017) | M3 | Further Dynamics | Elastic springs and strings | - |
| Edexcel A2 Further Maths 2017 | Further Mechanics 1 | Elastic Strings, Springs and Energy | Elastic Springs and Strings | - |
| Edexcel AS/A2 Further Maths 2017 | Further Mechanics 1 | Elastic Strings, Springs and Energy | Elastic Springs and Strings | - |
| OCR A-Level (UK - Pre-2017) | M3 | Further Dynamics | Elastic springs and strings | - |
| OCR A2 Further Maths 2017 | Mechanics | Work, Energy and Power | Elastic Springs and Strings | - |
| OCR MEI A2 Further Maths 2017 | Mechanics B | Hooke's Law | Elastic Springs and Strings | - |
| OCR-MEI A-Level (UK - Pre-2017) | M3 | Further Dynamics | Elastic springs and strings | - |
| Universal (all site questions) | F | Further Dynamics | Elastic springs and strings | - |
| WJEC A-Level (Wales) | M3 | Further Dynamics | Elastic springs and strings | - |