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I'm was going through the simple harmonic oscillator, just as a recap, and I stumbled upon something which is causing me wonder.

I'm solving the SHO with a shifted origin, and so I have the differential equation

[tex]F=-k(x-x_0)[/tex]

[tex]\ddot{x}=-\frac{k}{m}x+\frac{kx_0}{m}[/tex]

Now, I get that I can solve the physics problem by simply setting X = x-x_0 and then just adding the normal solution to x_0 to get the position of the particle, however, I was wondering, is it possible to solve the differential equation as it stands above and directly get a solution for x?

Thanks in advance!

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# Harmonic oscillator shifted origin

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