previous    next

Oscillations

Period, frequency and angular frequency

Every time that the oscillating body completes one cycle, the uniform circular motion completes one cycle. The time t=T it takes for the oscillating body to complete one cycle is called the period of the oscillation. Consequently, one has

ωT = 2π    →    ω = 2π/T

The frequency f is the amount of times that the oscillating body completes cycles in one unit of time (1 second). Consequently, one has

f = 1/T    →    ω = 2πf

Hence, the angular velocity ω of the uniform circular motion which completes cycles in the same rythme as the oscillating body equals 2π times the frequency f of the oscillating body. For that reason one also uses the expression angular frequency in referring to ω.

Motion for which the displacement can be described by sine or cosine functions linear in t is called simple harmonic motion.

Hooke's law