Question

$block \: is \: at \: rest \ \\ spring \: is \: in \: natural \: length. \\ find \: the \: maximum \: displacement \: of \: the \: block$
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Answer 1

$w.all \: the \: forces = kinetic \: energy \\ w.spring + w.gravity + w.tension = kinetic \: energy \\ \\ - \frac{1}{2} k( {(2x)}^{2} - 0) + mg(x) = 0 \\ - k2 {x}^{2} + mg(x) = 0 \\ mg(x) = 2 {x}^{2} k \\ x = \frac{mg}{2k}$

Answer 2

$\huge\bf{Answer:-}$

Refer the attachment.