The motion of a mass on a spring, with spring constant $$K$$ is as shown in 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 mass is $$x(0)$$ and velocity $$v(0)$$, then its displacement can also be represented as $$x(t) = C\cos(\omega t - \phi)$$, where $$C$$ and $$\phi$$ are:

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

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

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

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