Question

solve this attachment ✍️✍️✍️

Answer 1

$\huge \mathfrak {Answer:-}$

Check this attachment

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Answer 2

$\underline{\underline{\Huge\mathfrak{Answer ;}}}$

Dear ,

Your Solution ⏬

$= > ax^{2} + bv^{2} = k$

$= > {bv}^{2} = k \: - {ax}^{2}$

$= > {v}^{2} = \frac{k}{b} - \frac{ax^{2} }{b}$

$= > v = \sqrt{ \frac{k}{b} - \frac{ax^{2} }{b} }$

We know that ;-
Maximum amplitude is when velocity is Zero ( 0 ).

So ,

$= > \sqrt{ \frac{k}{b} - \frac{ax^{2} }{b} } = 0$

$= > \frac{ {ax}^{2} }{b} = \frac{k}{b}$

$= > {ax}^{2} = k$

$= > x = \sqrt{ \frac{k}{a} }$

__________________________

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@ItsDmohit