Understanding Swing Movement: Calculating Distance and Time in a Pendulum Swing

Feb 07, 2026

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This problem explores the movement of a swing that oscillates between two points. The swing moves a total distance of 2 meters, completing one full swing in π seconds, starting at point A. The horizontal distance from the center is defined by the equation d = Cos(4t), where d represents the distance at time t in seconds. The challenge is to determine the first instance when the swing is 0.6 meters from point A. Using the equation, we find that this occurs at t = 0.29 seconds (to 2 decimal places), demonstrating the relationship between time and position in harmonic motion.

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Understanding Swing Movement: Calculating Distance and Time in a Pendulum Swing

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Home End Swing Problem A swing moves a distance of 2m from one side to the other One complete swing movement takes πseconds. The swing starts at point ‘A’ A The equation for the distance d = Cos(4t) where t = time in seconds & d = horizontal distance from the centre point B B A When is the first time the swing is 0.6m from point ‘A’?
Home End Swing Problem A swing moves a distance of 2m from one side to the other One complete swing movement takes πseconds. The swing starts at point ‘A’ A 0.6m The equation for the distance d = Cos(4t) where t = time in seconds & d = horizontal distance from the centre point d = 0.4 B B A Solve 0.4 = Cos(4t) 4t = Cos-1 0.4 When is the first time the swing is 0.6m from point ‘A’? 4t = 1.159 t = 1.159 ÷ 4 = 0.29sec (2dp)