A machine is subjected to the motion \(x(t)=A \cos (50 t+\alpha) \mathrm{mm}\). The initial conditions are given by \(x(0)=3 \mathrm{~mm}\) and \(\dot{x}(0)=1.0 \mathrm{~m} / \mathrm{s}\).

a. Find the constants \(A\) and \(\alpha\).

b. Express the motion in the form \(x(t)=A_{1} \cos \omega t+A_{2} \sin \omega t\), and identify the constants \(A_{1}\) and \(A_{2}\).