v₀ = v(t = 0) and x₀ = x(t = 0) in general.

v₀ = 0 ms^-1 and x₀ = x(t = 0) in the case of over-damped oscillators.

v₀ = v(t = 0) and x₀ = 0 m in general.

v₀ = 0 ms^-1 and x₀ = 0 m in the case of under-damped oscillators.

v₀ = 0 ms^-1 and x₀ = x(t = 0) in general.

v₀ = 0 ms^-1 and x₀ = 0 m in the case of undamped simple harmonic oscillators.

v₀ = v(t = 0) and x₀ = 0 m in the case of critically-damped oscillators.