In the course of solving the simple harmonic oscillator, one reaches a fork in the road.(adsbygoogle = window.adsbygoogle || []).push({});

x(t) = A1Sin(wt) + A2Cos(wt)

At this point, you exploit a trig identity and arrive at one of two solutions

x(t) = B1Sin(wt+phi1)

or

x(t) = B2Cos(wt+phi2)

Both of these are correct solutions and either one can be used to suit the particular problem. However, convention usually has us using Sin instead of Cos. Is there any particular reason for this? Is it to exploit the small angle / taylor series approximation?

Sin(x) ≈ x - (x^3)/6

Cos(x) ≈ 1 - (x^2)/2

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# Why is Sin the convention for the harmonic oscillator?

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