The formula to calculate the kinetic energy $\left(K\right)$ of a particle executing SHM is given by

$K\mathit{=}\frac{\mathit{1}}{2}k\left(A^2\mathit{-}{y}^2\right) ...\left(1\right)$

Substitute the values of the known parameters into equation (1) and solve to calculate the value of the unknown parameter.

$\begin{array}{rcl}K& =& \frac{1}{2}\times k\times \left(A^2-A^2{\cos }^{2}30°\right)\\ & =& \frac{1}{2}\times k\times A^2{\sin }^{2}30°\\ & \Rightarrow & 200=\frac{1}{2}\times 1.0\times {10}^x\times {\left(0.4\right)}^2\times {\left(\frac{1}{2}\right)}^2\\ & =& \frac{2\times {10}^x}{100}\\ & \Rightarrow & {10}^2={10}^{x-2}\\ & \Rightarrow & x-2=2\\ & \Rightarrow & x=4\end{array}$