MAE 4182 · After-class practice
Frequency response · practice
Understand the signals, calculate the response, read the plots, then try two sketches.
Q1 · Read the two sine waves
r(t) = 3 sin(2t), yss(t) = 1.5 sin(2t − π/4)
Identify amplitude, angular frequency, period, and phase. Then state what changed between input and output.
Formulas for this practice
r(t) = R sin(ωt) · T = 2π/ω
yₛₛ(t) = Y sin(ωt + φ) · Y = R|G(iω)| · φ = ∠G(iω)
Find G(iω) by substituting s = iω. |a + ib| = √(a² + b²)
∠(a + ib) = tan⁻¹(b/a) for a > 0. ∠(z₁/z₂) = ∠z₁ − ∠z₂
Step 1 of 6
Read the input
Match r(t) to R sin(ωt). Which number sets the height, and which number sets the rate of oscillation?
Jump to a step:
Given waveforms
r(t) = 3 sin(2t)
yss(t) = 1.5 sin(2t − π/4)
Useful formulas
r(t) = R sin(ωt)
yss(t) = Y sin(ωt + φ)
T = 2π/ω 180° = π rad
Y = R |G(iω)| φ = ∠G(iω)
|G(iω)| = Y/R
R: input amplitude · Y: output amplitude · ω: angular frequency · φ: phase shift