Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Derivations from Pendulum (mathematics). To begin, we shall make three assumptions about the simple pendulum: The rod/string/cable on which the bob is swinging is massless, does not stretch, and always remains taut. The bob is a point mass. Motion occurs in a 2-dimensional plane, i.e. pendulum does not swing into and out of the page. Consider Figure 1, showing the forces acting on a simple pendulum. Note that the path of the pendulum sweeps out an arc of a circle. The angle is measured in radians, and this is crucial for this formula. The blue arrow is the gravitational force acting on the bob, and the violet arrows are that same force resolved into components parallel and perpendicular to the bob's instantaneous motion. The direction of the bob's instantaneous velocity always points along the red axis, which is considered the tangential axis because its direction is always tangent to the circle. Consider Newton's second law,

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