Period

Symbol $T$, unit the second. One quantity, two senses.

• Oscillation. $T$ is the time for the object to return to the same position moving the same way. AP Physics 1 EK 7.2.A.1 ties it to frequency by $T = 1/f$, then gives $T_s = 2\pi\sqrt{m/k}$ for an ideal spring and object and $T_p = 2\pi\sqrt{\ell/g}$ for a simple pendulum at small angle.
• Wave. AP Physics 2 EK 14.2.A.1.i calls the period the time for one complete oscillation of the wave. Watch one point in the medium and $T$ is how long that point takes to get back to where it started.

$T = 1/f$ is printed on the AP Physics 1, AP Physics 2 and AP Physics C sheets. The C: Mechanics sheet prints the longer form $T = 2\pi/\omega = 1/f$.

Two traps. Period does not depend on amplitude (EK 7.3.A.2). And a repeat distance read off a displacement-against-position graph is not a period: that graph shows wavelength. Only a graph with time on the horizontal axis shows $T$.

How period, frequency, wavelength and speed convert into each other is worked through in the wave speed guide.