What is Amplitude and phase?

In $x(t) = A\cos(2\pi t/T_0 + \varphi)$ the positive constant $A$ is the amplitude — the extremes are $x = \pm A$ — and $2\pi t/T_0 + \varphi$ is the phase, growing by $2\pi$ each period; the initial phase $\varphi$ records the start: released at rest from $x = A$, $\varphi = 0$. For instance $m = 0.20\,\mathrm{kg}$ on $k = 20\,\mathrm{N}/\mathrm{m}$ gives $T_0 = 2\pi\sqrt{0.20/20} = 0.63\,\mathrm{s}$; pulled to $5.0\,\mathrm{cm}$ and released, $x(t) = 5.0\cos(2\pi t/0.63)$ in centimeters.