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

\(v_1=3 \,m / s x_1=4 \,m\)

\(v_2=4 \,m / s x_2=3 \,m\)

\(3=\omega \sqrt{A^2-4^2} \ldots(i)\)

\(4=\omega \sqrt{A^2-3^2} \ldots(ii)\)

Solving \((i)\) and \((ii)\), we get

\(A=5 \,m\) and \(\omega=1 \,rad / s\)