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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
satisfy this condition, so we pick14 the phase to be φ = π . Hence, the equation of motion
is x(t) = 3 sin 2t + π . To ﬁnd when the object passes through the equilibrium position we
solve x(t) = 3 sin 2t + π = 0. Going through the usual analysis we ﬁnd t = − π + π k for
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
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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