The motion of a mass on a spring,with spring constant $K$ is as shown in the figure. The equation of motion is given by $x(t) = A \sin \omega t + B \cos \omega t$ with $\omega = \sqrt{\frac{K}{m}}$. Suppose that at time $t = 0$,the position of the mass is $x(0)$ and velocity is $v(0)$,then its displacement can also be represented as $x(t) = C \cos (\omega t - \phi)$,where $C$ and $\phi$ are:

• A
  $C = \sqrt{\frac{2 v(0)^2}{\omega^2} + x(0)^2}, \phi = \tan^{-1} \left( \frac{x(0) \omega}{2 v(0)} \right)$
• B
  $C = \sqrt{\frac{v(0)^2}{\omega^2} + x(0)^2}, \phi = \tan^{-1} \left( \frac{x(0) \omega}{v(0)} \right)$
• C
  $C = \sqrt{\frac{2 v(0)^2}{\omega^2} + x(0)^2}, \phi = \tan^{-1} \left( \frac{v(0)}{x(0) \omega} \right)$
• D
  $C = \sqrt{\frac{v(0)^2}{\omega^2} + x(0)^2}, \phi = \tan^{-1} \left( \frac{v(0)}{x(0) \omega} \right)$