- #1
Taylor_1989
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- 14
Homework Statement
Hi guys I am having a problem deriving this solution for a simply pendulum. Could someone please help me.
My issue is taking the second order and getting into just cos. I have attempted a solution which is shown below.
Homework Equations
The Attempt at a Solution
$$\theta^{''}+\frac{g}{l}\theta=0$$
$$ p^2+\frac{g}{l}\theta=0$$
$$\omega^2=\frac{g}{l}$$
So general solution: $$\theta (t) = Ae^{i\sqrt{\omega t }}+Be^{-i\sqrt{\omega t }}$$[/B]using the fact that: $$e^{(\pm) i \omega t}=cos{\omega t}\pm sin{i\omega t }$$
I get the general equation:
$$\theta (t)= (A+B)cos(\omega t)+ i(A-B)sin(\omega t)$$
I am now confused on what to do next. I was thinking that beacuse I am only looking for real values the i component would be equal to 0. But I do no think this is the case, I am just really can't figure why.
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