17. Periodic Motion
Simple Harmonic Motion of Pendulums
7:24 minutes
Textbook Question
Textbook QuestionIn Section 14–5, the oscillation of a simple pendulum (Fig. 14–48) is viewed as linear motion along the arc length 𝓍 and analyzed via F = ma. Alternatively, the pendulum’s movement can be regarded as rotational motion about its point of support and analyzed using T = Iα . Carry out this alternative analysis and show that θ (t) = θₘₐₓ cos ( √g/ℓ t + θ) ,
where θ (t) is the angular displacement of the pendulum from the vertical at time t, as long as its maximum value is less than about .
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