The motion of a mass on a spring, with spring constant K is as...

x = Asin\omegat + Bcos\omegat$<br />$v = \dfrac{dx}{dt} = A\omega cos\omegat - B\omega sin\omegat$<br />At$t = 0, x ( 0 ) = B$<br />$v ( 0 ) = A\omega$<br />$x = Asin\left(\omega + Bsin\left(\omegat + 90 °\right)\right)

${A}_{net} = \sqrt{{A}^{2} + {B}^{2}}$
$tan\alpha = \dfrac{B}{A} ⇒ cot\alpha = \dfrac{A}{B}$
$⇒ x = \sqrt{{A}^{2} + {B}^{2}}\sin ( \omegat + \alpha )$
$⇒ x = \sqrt{{A}^{2} + {B}^{2}}\cos ( \omegat - ( 90 - \alpha ) )$

$x = Ccos ( \omegat - ϕ )$

$⇒ C = \sqrt{{A}^{2} + {B}^{2}}$

$C = \sqrt{\dfrac{[ v ( 0 ) {]}^{2}}{{\omega}^{2}} + [ x ( 0 ) {]}^{2}}$
$ϕ = 90 - \alpha$
$tan\alpha = cos\alpha = \dfrac{A}{B}$

$⇒ tanϕ = \dfrac{v ( 0 )}{x ( 0 ) \cdot \omega}$
$ϕ = \tan^{- 1}\left(\dfrac{v ( 0 )}{x ( 0 ) \omega}\right)$