Derivation of simple pendulum formula

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The discussion focuses on calculating the time it takes for a simple pendulum, with a length of 0.240 m, to reach its highest speed when released from angles of 3.5 degrees and 1.75 degrees. It emphasizes the use of small angle approximation to derive a differential equation for the pendulum's motion. A free body diagram is suggested to aid in visualizing the forces acting on the pendulum bob. The calculations will differ based on the initial angle of release, impacting the time to reach maximum speed. Understanding these dynamics is crucial for accurately modeling pendulum motion.
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You pull a simple Pendulum of length 0.240 m to the side through an angle of 3.5 degrees and release it.
(a) How much time does it take the pendulum bob to reach its highest speed?
(b) How much time does it take if the pendulum is released at an angle 1.75 degrees instead of 3.5 degrees?
 
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Draw a free body diagram so you can write the differential equation for the motion of the pendulum bob. Assume small angle of swing so you can get a differential equation that you can easily solve.
 

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