Taking the Laplace transforms of v and p with respect to time yields v ^ ^ ( r , s ) = v m s cos ⁡ ⁡ φ φ v , 0 − − ω ω sin ⁡ ⁡ φ φ v , 0 s 2 + ω ω 2 , p ^ ^ ( r , s ) = p m s cos ⁡ ⁡ φ φ p , 0 − − ω ω sin ⁡ ⁡ φ φ p , 0 s 2 + ω ω 2 .