A pendulum is swung (20 mathrm{~cm}) and allowed to swing freely until it eventually comes to rest.

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A pendulum is swung \(20 \mathrm{~cm}\) and allowed to swing freely until it eventually comes to rest. Each subsequent swing of the bob of the pendulum is \(90 \%\) as far as the preceding swing. How far will the bob travel before coming to rest?

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