c
(c)

\(A=2 \,cm =2 \times 10^{-2}\)

\(a=-\omega^2 x\)

and \(v=\omega \sqrt{A^2-x^2}\)

\(\omega^2 \times 1 \times 10^{-2}=\omega \sqrt{(4-1) 10^{-4}}\)

\(\omega \times 1 \times 10^{-2}=\sqrt{3} \times 10^{-2}\)

\(\omega=\sqrt{3}\)

\(T=\frac{2 \pi}{\omega}=\frac{2 \pi}{\sqrt{3}}\)