c
General equation for displacement is given by

\(x=A \sin (\omega t+\phi)\)

\(\text { at given time }\)

\(\Rightarrow \omega t+\phi=30^{\circ}\)

\(\Rightarrow x=40 \times \frac{\sqrt{3}}{2} \Rightarrow 20 \sqrt{3}\,cm\)

\(\Rightarrow A=40\,cm\)

\(\Rightarrow K . E=\frac{1}{2} k\left(A^2-x^2\right)=200\)

\(200=\frac{1}{2} k\left(\frac{1600-1200}{100 \times 100}\right)\)

\(400 \times 100 \times 100=k \times 400\)

\(k=10^4\)

\(x=4\)