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skyesthelimit

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For a harmonic oscillator with a restoring force with F= -mω

^{2}x, I get that the solution for the x-component happens at x=exp(±iωt). But why is it that you can generalise the solution to x= Ccosωt+Dsin(ωt)? Where does the sine term come from because when I use Euler's formula, the only real part seems to be the cosine term?
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