g-l-sin-0-Find-the-exact-solution-

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

\overset{. .}{θ} + \frac{g}{l} s i n θ = 0 (F i n d t h e e x a c t s o l u t i o n)

Answered by Olaf last updated on 29/Nov/20

\overset{∙ ∙}{θ} + \frac{g}{l} \sin θ = 0 (1)

(1) \times \overset{∙}{θ} : \overset{∙ ∙}{θ} \overset{∙}{θ} + \frac{g}{l} \overset{∙}{θ} \sin θ = 0

\Rightarrow \frac{1}{2} \overset{∙ 2}{θ} - \frac{g}{l} \cos θ = C (2)

Usually at t = 0, θ = θ_{0}, \overset{∙}{θ} = 0

\Rightarrow C = - \frac{g}{l} \cos θ_{0}

(2) : \frac{\overset{∙}{θ}}{\sqrt{\cos θ - \cos θ_{0}}} = \sqrt{\frac{l}{g}}

\dots to be continued \dots

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