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Question Number 123858 by Dwaipayan Shikari last updated on 28/Nov/20

$$\stackrel{..}{\theta }+\frac{g}{l}sin\theta =0\left(Findtheexactsolution\right)$$

Answered by Olaf last updated on 29/Nov/20

$$\stackrel{\bullet \bullet }{\theta }+\frac{g}{l}\sin \theta =0\left(1\right)$$$$\left(1\right)\times \stackrel{\bullet }{\theta }:\stackrel{\bullet \bullet }{\theta }\stackrel{\bullet }{\theta }+\frac{g}{l}\stackrel{\bullet }{\theta }\sin \theta =0$$$$\Rightarrow \frac{1}{2}\stackrel{\bullet 2}{\theta }-\frac{g}{l}\cos \theta =\mathrm{C}\left(2\right)$$$$\mathrm{Usually}\mathrm{at}t=0,\theta ={\theta }_0,\stackrel{\bullet }{\theta }=0$$$$\Rightarrow \mathrm{C}=-\frac{g}{l}\cos {\theta }_0$$$$\left(2\right):\frac{\stackrel{\bullet }{\theta }}{\sqrt{\cos \theta -\cos {\theta }_0}}=\sqrt{\frac{l}{g}}$$$$...\mathrm{to}\mathrm{be}\mathrm{continued}...$$

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