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 ω t+B cos ω t with…

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