17.1.4—The equations v = v0 cos ωt and v = ± ω ()xx0 22−

For x=x₀sinωt, v=x₀ωcosωt and v²=ω²(x₀²−x²), with the sign of v set by direction of motion.

Use the time form for phase questions and the squared form when only position and speed magnitude are known.

At x=0 the speed is maximum v₀=ωx₀; at x=±x₀ the speed is zero.

The ± sign in v=±ω√(x₀²−x²) cannot be chosen without considering the direction of travel.