Given transfer function, the identified correct steady-state response ys(t) to the given input function is: y (t) = 27.116 Sin (1.5 t - 49.4°)
<h3>What is a transfer function?</h3>
A transfer function is a mathematical link between a numerical input to a dynamic system and the subsequent output in statistical time-series analysis, signal processing, and control engineering.
<h3>What is the calculation justifying the above result?</h3>
Step 1
Recall that we are given T(s) = Ys)/F(s) = 75/(145 + 18)
⇒ T(Jw) = 75/ [18 + J14w]
This is called a steady state response to Sinusoidal input.
f(t) = [T(t) ↔T(jw)] → y(t A Sin (wi + φ)
Where A = A1 x [T(jw)] w= w1
⇒ A = A1 [T(jw1)]
And,
φ = θ + [T(jw)] w = w1
Step 2
Given, f(t) = 10 Sin 1.5t
A1 = 10, W1 = 1.5 red/see, θ = 0°
The Magnitude of T(jw) is
[T(jw)] = 75/√[(18²) + (14w)²
⇒ [T(jw] w = w1 = 1.5
= 75/√[(18²) + (141.5)²
⇒ [T(jw1)] = 2.7116
Hence,
A = A1 x [T(jw1)] =
10 x 2.7116
⇒ A = 2.116
⇒ Phase of T(jw) is,
[T(jw)] = - tan ⁻¹ (14w/18)
Hence, φ = 0° - Tan⁻1 (21/18)
φ = -49.4°
Hence,
y(t) = A sin (w1t + φ)
⇒ y (t) = 27.116 Sin (1.5 t - 49.4°)
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