At a given point of time the value of displacement of a simple...

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

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

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

$\begin{cases}K & = & \dfrac{1}{2} \times k \times \left({A}^{2} - {A}^{2}\cos^{2}30 °\right) \\ & = & \dfrac{1}{2} \times k \times {A}^{2}\sin^{2}30 ° \\ & ⇒ & 200 = \dfrac{1}{2} \times 1 . 0 \times {10}^{x} \times {\left(0 . 4\right)}^{2} \times {\left(\dfrac{1}{2}\right)}^{2} \\ & = & \dfrac{2 \times {10}^{x}}{100} \\ & ⇒ & {10}^{2} = {10}^{x - 2} \\ & ⇒ & x - 2 = 2 \\ & ⇒ & x = 4\end{cases}$