For any simple harmonic motion, the position, velocity, and acceleration can all be written as the same type of trigonometric function (sine or cosine) by correctly adding a relative phase factor. an x component of the position function given by x(t)=βcos(ωt+δ) is a valid general solution for simple harmonic motion. part a write the x component of the velocity associated with this position function. express your answer in terms of some or all of the variables β, ω, δ and t.