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The horizontal displacement, \(D\) cm, of the bob of a pendulum from its central position is modelled by a sine function of time, \(t\) seconds. The bob is released from its maximum displacement of 10 cm at \(t=0.25\) seconds. It swings to a minimum displacement of -10 cm and first returns to its maximum displacement at \(t=1.25\) seconds.
Find a sine function of the form \(D(t) = a\sin(b(t-c)) + d\) to model this motion.
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