Final answer:
To calculate the gain at ω = 8.8 rad/s, substitute the value of s as jω in the transfer function and simplify the expression to find |T(jω)| ≈ 2.162.
Step-by-step explanation:
The transfer function of a dynamical system is given by T(s) = 2/(a + 2s), with a = 4.3. To calculate the gain at ω = 8.8 rad/s, we need to substitute the value of s as jω in the transfer function. In this case, s = j(8.8).
Substituting s = j(8.8) in the transfer function:
T(jω) = 2/(a + 2jω) = 2/(4.3 + 2j(8.8))
Next, we need to rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator:
T(jω) = (2/(4.3 + 2j(8.8))) * ((4.3 - 2j(8.8))/(4.3 - 2j(8.8)))
Simplifying the expression:
T(jω) = (17.2 - 35.2j)/(4.3^2 + (2*8.8)^2)
Finally, we calculate the magnitude of the complex number:
|T(jω)| = √((17.2^2) + (-35.2^2))/(4.3^2 + (2*8.8)^2)
|T(jω)| = √(298.64 + 1239.04)/(18.49 + 310.72)
|T(jω)| = √(1537.68)/(329.21)
|T(jω)| = √4.672
|T(jω)| ≈ 2.162