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.

Contents

 * 1) /Elastic Strings and Springs/
 * 2) /Impulse and Momentum/
 * 3) /Circular Motion/
 * 4) /Kinematics/
 * 5) Simple Harmonic Motion

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

 * $$\ddot{x} = -\omega ^2x$$
 * $$v^2 = \omega ^2(a^2-x^2)\,$$
 * $$T = \frac{2\pi}{\omega}$$
 * $$x = a \sin (\omega t)\,$$ 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
only applies when $$ \theta $$ is in radians
 * $$\sin \theta \approx \theta$$
 * $$\cos \theta \approx 1 - \frac{1}{2}\theta ^2 $$
 * $$ \tan \theta \approx \theta $$