(Solution) - A simple pendulum of length L is released from rest -(2025 Original AI-Free Solution)

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A simple pendulum of length L is released from rest from an angle f0.
(a) Assuming that the pendulum undergoes simple harmonic motion, find its speed as it passes through f = 0.
(b) Using the conservation of energy, find this speed exactly.
(c) Show that your results for (a) and (b) are the same when f0 is small.
(d) Find the difference in your results for f0 = 0.20 rad and L = 1 m.