# Physics equations/07-Work and Energy/A:pendulum

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## Wikilab: Energy and the pendulum[edit]

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By definition, angular frequency and period are related by,

This lab employs two approximation that are valid when :

Use the Excel spreadsheet to plot the sine and cosine functions for θ between zero and one, taking approximately 20 increments within that interval.

Copy and paste your page onto the same excel spreadsheet and verify that a better approximation is:

Consider a pendulum of length *L* situated so that the equilibrium point is at the origin. Make a careful hand drawing showing that:

Use this to show that an approximate formula for the energy of a pendulum is:

Defining as the *effective spring constant*, this energy can be expressed in familiar form: