I'm trying to work out the differential equation for simple harmonic motion without damping,(adsbygoogle = window.adsbygoogle || []).push({});

[itex]x''+\frac{k}{m}x = 0[/itex]

I can solve it to

[itex]x = c_1cos(\sqrt{\frac{k}{m}}) + c_2sin(\sqrt{\frac{k}{m}})[/itex]

But the generalized solution is

[itex]x = Acos(\omega*t + \delta)[/itex]

where

[itex]A = \sqrt{c_1^2 + c_2^2}[/itex]

I can understand the change of variables, but I don't really understand what happens to the sine term. Can anyone help me with this?

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# Harmonic Motion Equation

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