A machine is subjected to the motion x(t) = A cos(50t + ) mm. The initial conditions are given by x(0) = 3 mm and

A machine is subjected to the motion x(t) = A cos(50t + α) mm. The initial conditions are given by

x(0) = 3 mm and x(0) = 1.0 m/s.

1. Find the constants A and α.
2. Express the motion in form x(t) = A1 cos ωt + A2 sin ωt, and identify the constants A1 and A2.