[<< wikibooks] 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 ==
Elastic Strings and Springs
Impulse and Momentum
Circular Motion
Kinematics
Simple Harmonic Motion

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

=== Kinematics ===

a
=
v

d
v

d
x

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

=== Simple Harmonic Motion ===

x
¨

=
−

ω

2

x

{\displaystyle {\ddot {x}}=-\omega ^{2}x}

v

2

=

ω

2

(

a

2

−

x

2

)

{\displaystyle v^{2}=\omega ^{2}(a^{2}-x^{2})\,}

T
=

2
π

ω

{\displaystyle T={\frac {2\pi }{\omega }}}

x
=
a
sin
⁡
(
ω
t
)

{\displaystyle x=a\sin(\omega t)\,}
or

x
=
a
cos
⁡
(
ω
t
)

{\displaystyle x=a\cos(\omega t)\,}
or, generally,

x
=
a
cos
⁡
(
ω
t
+
ϵ
)

{\displaystyle x=a\cos(\omega t+\epsilon )\,}

=== Elastic Springs and Strings ===
Hooke's Law:

T
=

λ
x

l

{\displaystyle T={\frac {\lambda x}{l}}}

Elastic potential energy:

E

p

=

λ

x

2

2
l

{\displaystyle E_{p}={\frac {\lambda x^{2}}{2l}}}

=== Small-angle Approximations ===

sin
⁡
θ
≈
θ

{\displaystyle \sin \theta \approx \theta }

cos
⁡
θ
≈
1
−

1
2

θ

2

{\displaystyle \cos \theta \approx 1-{\frac {1}{2}}\theta ^{2}}

tan
⁡
θ
≈
θ

{\displaystyle \tan \theta \approx \theta }
only applies when

θ

{\displaystyle \theta }
is in radians