Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: s here are carried over from Physics. If not for the spring, the object would fall towards the ground, which is the ‘natural’ or ‘positive’ direction. Since the spring force acts in direct opposition to gravity, any movement upwards is considered ‘negative’. 754 Applications of Trigonometry which in this case gives 3 sin(φ) = 3 so sin(φ) = 1. Only φ = π and angles coterminal to it 2 satisfy this condition, so we pick14 the phase to be φ = π . Hence, the equation of motion 2 is x(t) = 3 sin 2t + π . To ﬁnd when the object passes through the equilibrium position we 2 solve x(t) = 3 sin 2t + π = 0. Going through the usual analysis we ﬁnd t = − π + π k for 2 4 2 integers k . Since we are interested in the ﬁrst time the object passes through the equilibrium position, we look for the smallest positive t value which in this case is t = π ≈ 0.78 seconds 4 after the start of the motion. Common sense suggests that if we release the object below the equilibrium position, the objec...
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