(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This problem relates to a mass on a spring, or most any SHM. For an undamped free vibration, I can solve the problem and reduce it to this equation:

[itex]l = Acoswt + Bsinwt[/itex] (1)

I know the equation is correct. I also know that the above equation reduces to:

[itex] Rcos(wt -\delta)[/itex] (2)

Sad to say, I can not figure out how 1 reduces to 2 (though simple it should be)! There is the trig identity

cos(x-y) = cosx*siny + sinx*cosy

but I am uncertain as to whether this helps in this particular case. I also believe that

[itex]R^2 = A^2 + B^2[/itex]

and so putting everything together I *should* be able to reduce 1 to 2, but alas have failed. If someone can explain the steps, that would be appreciated :)

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# Homework Help: Diff. Eq. related to SHM question

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