← all cardsTopic 8 · Oscillations · Definitions
Period, frequency & ω
● VERBATIM — examined word-for-wordPeriod T: time for one complete oscillation. Frequency f: number of complete oscillations per unit time.
f = 1/T · ω = 2πf = 2π/TWhat this actually means
T is seconds per cycle, f is cycles per second, and ω is the same rhythm expressed as phase per second: 2π of phase every cycle.
ω is the workhorse because the mathematics of SHM is written in angles: x = x₀ sin ωt only works with ω in rad s⁻¹ and the calculator in radian mode.
Given any one of T, f, ω you have all three. Convert without thinking.
Prove it — watch it be true
- Read T off the x–t graph, peak to peak
- Compute f = 1/T and ω = 2π/T
- One cycle of the graph = 2π of phase, whatever the amplitude