(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 :)

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Diff. Eq. related to SHM question

**Physics Forums | Science Articles, Homework Help, Discussion**