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**Driven Damped Harmonic Oscillator, f != ma??**

Let's say I've got a driven damped harmonic oscillator described by the following equation:

[tex]A \ddot{x} + B \dot{x} + C x = D f(t)[/tex]

given that [tex] f = ma[/tex] why can't I write

[tex]A \ddot{x} + B \dot{x} + C x = D ma[/tex]

substitute [tex]\ddot{x} = a[/tex] to get

[tex]A \ddot{x} + B \dot{x} + C x = D m \ddot{x}[/tex]

and then rearrange to get

[tex](A - D m) \ddot{x} + B \dot{x} + C x = 0[/tex]

I know that's not how the problem is solved, but what is to stop me from solving it that way?

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