A simple pendulum of length (0.30 mathrm{~m}) has a (0.30-mathrm{kg}) bob. At (t=0), the bob passes through

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A simple pendulum of length \(0.30 \mathrm{~m}\) has a \(0.30-\mathrm{kg}\) bob. At \(t=0\), the bob passes through the lowest position in its motion, and at this instant it has a horizontal speed of \(0.25 \mathrm{~m} / \mathrm{s}\).

(a) What is the maximum angular displacement \(\vartheta_{\max }\) away from vertical that the pendulum reaches?

(b) What is the bob's linear speed \(v\) when it has angular displacement \(\vartheta_{\max } / 2\) ?

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