Editing Simple harmonic motion (section)

===Mass of a simple pendulum===
{{Infobox physical quantity
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| caption = A [[pendulum]] making 25 complete [[oscillation]]s in 60 s, a frequency of 0.41{{overline|6}} [[Hertz]]
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In the [[small-angle approximation]], the [[pendulum (mechanics)#Small-angle approximation|motion of a simple pendulum]] is approximated by simple harmonic motion. The period of a mass attached to a pendulum of length {{math|''l''}} with gravitational acceleration <math>g</math> is given by
<math display="block"> T = 2 \pi \sqrt\frac{l}{g}</math>

This shows that the period of oscillation is independent of the amplitude and mass of the pendulum but not of the acceleration due to [[gravity]], <math>g</math>, therefore a pendulum of the same length on the Moon would swing more slowly due to the Moon's lower gravitational field strength. Because the value of <math>g</math> varies slightly over the surface of the earth, the time period will vary slightly from place to place and will also vary with height above sea level.

This approximation is accurate only for small angles because of the expression for [[angular acceleration]] {{math|''α''}} being proportional to the sine of the displacement angle:

<math display="block">-mgl \sin\theta =I\alpha,</math>

where {{math|''I''}} is the [[moment of inertia]]. When {{math|''θ''}} is small, {{math|sin ''θ'' ≈ ''θ''}} and therefore the expression becomes

<math display="block">-mgl \theta =I\alpha</math>

which makes angular acceleration directly proportional and opposite to {{math|''θ''}}, satisfying the definition of simple harmonic motion (that net force is directly proportional to the displacement from the mean position and is directed towards the mean position).