A block rests on an inclined plane. A spring is attached is a pulley and is pulled downward gradually with increasing force. $\mu$ is the coefficient of friction between block and inclined plane . Find the potential energy of the spring at the momentum when block begins to move for a force constant k of spring $[\theta= 30^{\circ}]$

Question

$a)\; k\;mg \bigg[\frac{1}{2}+\frac{\sqrt 3 \mu}{2} \bigg]^2 \\ b)\;\frac{m^2g^2\bigg[\frac{\sqrt 3}{2}+\frac{\mu}{2}\bigg]^2}{2k} \\ c)\; \frac{k^2 m^2}{g^2}\bigg[\frac{1}{2}+\frac{\sqrt 3}{2} \mu\bigg]^2 \\ d)\; \frac{m^2g^2\bigg[\frac{1}{2}+\frac{\sqrt 3}{2} \mu\bigg]^2}{2 k}$