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Observe the motion of the point, E, around the circle. The angle EOP is increasing at a constant rate. Describe the motion of point X.
Please enable Java for an interactive construction (with Cinderella).

Summary/Background

• the distance OP is called the amplitude
• the velocity of x is written as \dot{x} and is greatest at O
• the velocity \dot{x} is zero at P and P'
• the acceleration \ddot{x} is zero at O
• the acceleration \ddot{x} is greatest at the end points P and P'.
• this motion is called simple harmonic motion (SHM)
• the angle \theta is increasing at a constant rate written as \dot{\theta} =\omega
• the equation \ddot{x} = -\omega^2 x describes the motion

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.

circle

a conic curve with equation (x-a)²+(y-b)²=r²

constant

a value in a formula or equation that cannot change.

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.

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)M2Motion in a circleAngular speed-
AQA AS Further Maths 2017MechanicsCircular MotionAngular Speed-
AQA AS/A2 Further Maths 2017MechanicsCircular MotionAngular Speed-
CCEA A-Level (NI)M2Motion in a circleAngular speed-
CIE A-Level (UK)M2Motion in a circleAngular speed-
Edexcel A-Level (UK - Pre-2017)M3Motion in a circleAngular speed-
Edexcel AS Further Maths 2017Further Mechanics 2Motion in a CircleAngular Speed-
Edexcel AS/A2 Further Maths 2017Further Mechanics 2Motion in a CircleAngular Speed-
OCR A-Level (UK - Pre-2017)M2Motion in a circleAngular speed-
OCR AS Further Maths 2017MechanicsMotion in a CircleAngular Speed-
OCR MEI A2 Further Maths 2017Mechanics BCircular MotionAngular Speed-
OCR-MEI A-Level (UK - Pre-2017)M3Motion in a circleAngular speed-
Universal (all site questions)MMotion in a circleAngular speed-
WJEC A-Level (Wales)M2Motion in a circleAngular speed-