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$ a)\; x \sqrt {\large\frac{m}{k_1}+\frac{m}{k_2}} \\ b)\; x \sqrt {\large\frac{k_1k_2}{m(k_1+k_2)}} \\ c)\; x \sqrt {\large\frac{k_1+k_2}{m}} \\ d) zero $

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Spring $k_1$ is compressed, and $k_2$ expanded by distance x

Using conservation of energy

the total potential energy of the spring= Kinetic energy of the mass

$\large\frac{1}{2}$$k_2x^2+\large\frac{1}{2}$$k_1x^2=\large\frac{1}{2}$$mv^2$

$v=x \sqrt {\large\frac{k_1+k_2}{m}}$

Hence cis the correct answer.

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