Pull an oscillator to full stretch, let go, and its displacement follows $x = A\cos\left(\dfrac{2\pi t}{T}\right)$ — read aloud: x equals A cosine of two-pi-t over T. Cosine is the right starter because $\cos 0 = 1$: at the moment of release the mass sits at full amplitude, exactly where you left it. (Later courses shorten $\dfrac{2\pi}{T}$ to $\omega$ — omega, the angular frequency — the same quantity in a trench coat.)

You rarely need a calculator, because the useful moments land on special angles: a quarter-cycle in, $\cos$ hits 0 (mid-crossing); half a cycle, $-1$ (far extreme); a full cycle, back to 1 (home). A sixth of a cycle gives exactly $\tfrac{1}{2}$, a third exactly $-\tfrac{1}{2}$. Five landmarks, and the whole curve is yours. What sets $T$ for a mass on a spring is its own clock, $T = 2\pi\sqrt{\dfrac{m}{k}}$ — more stuff swings slower, stiffer springs snap it back faster.