Phase Characteristics Homework Help, Assignment Help, Online Tutor, Tutoring

Submit Assignment

* *

Payment Online Assignment Help

Homework Help

sfsf

Phase Characteristics

An important feature of forced oscillations is the relation between the phase of displacement and that of external force. We find, if

F = F₀ cos ω t

then displacement q = A₀ cos (ω t – Ø)

Ø is the phase difference between force and displacement. If Ø > 0, displacement lags behind the applied force.

The dependence of Ø on frequency ω is called phase characteristics.

1. ω << ω₀: At very low frequencies, Ø is small and positive. That means, displacement lags behind the force by very small amount. As ω increases, the phase lag of displacement also increases.

2. ω = ω₀: At resonance, tan Ø = ∞, or Ø = π/2. The displacement lags behind the force by π/2. This means that when the force attains its maximum value, the displacement is zero, and vice-versa.

3. ω >> ω₀: As frequency ω further increases, the phase lag also increases. Displacement continues to lag behind the force and when ω becomes very large, we have At high driving frequencies, displacement is π out of phase with force. That is when force is maximum in one direction, displacement is maximum in opposite direction.

Note that at resonance both force and velocity are ahead of displacement by π/2; hence force and velocity are in phase. At ω = ω₀, F = F₀ cos ω t, q = – A₀ ω sin (ω t – π/2)

= A₀ ω cos ω t

The force and velocity oscillate in phase during resonance. During oscillations, force is always in the same direction as velocity and therefore energy of the oscillator increases; hence the power resonance.