A-level Mathematics/OCR/M3

This is the Mechanics 3 module of the A-level Mathematics book. This module assumes that you are familiar with the C1, C2, C3, C4, M1 and M2 modules. Please post all questions to A-level Mathematics/Discussion.

Formulae

By the end of this module you will be expected to have learnt the following formulae:

Kinematics

$a=v{\frac {dv}{dx}}$

Simple Harmonic Motion

${\ddot {x}}=-\omega ^{2}x$
$v^{2}=\omega ^{2}(a^{2}-x^{2})\,$
$T={\frac {2\pi }{\omega }}$
$x=a\sin(\omega t)\,$ or $x=a\cos(\omega t)\,$ or, generally, $x=a\cos(\omega t+\epsilon )\,$

Elastic Springs and Strings

Hooke's Law: $T={\frac {\lambda x}{l}}$
Elastic potential energy: $E_{p}={\frac {\lambda x^{2}}{2l}}$

Small-angle Approximations

$\sin \theta \approx \theta$
$\cos \theta \approx 1-{\frac {1}{2}}\theta ^{2}$
$\tan \theta \approx \theta$

only applies when $\theta$ is in radians

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Contents

Formulae

Kinematics

Simple Harmonic Motion

Elastic Springs and Strings

Small-angle Approximations