Final answer:
To calculate the magnitude of the transfer function H(w) at a specific frequency, substitute the frequency into the transfer function equation. In this case, H(0.5 Hz) = 9.4/(1+j(2π(0.5 Hz))). To find the magnitude, substitute the real and imaginary parts of H(0.5 Hz) into the formula for |z| = sqrt(a^2 + b^2).
Step-by-step explanation:
To calculate the magnitude of the transfer function H(w) at a specific frequency, we substitute the frequency value into the transfer function equation. In this case, the transfer function is H(w) = A/(1+jw) where A = 9.4. To find H(w) at f = 0.5 Hz, we substitute w = 2πf into the equation: H(w) = 9.4/(1+j(2πf)). So, H(0.5 Hz) = 9.4/(1+j(2π(0.5 Hz))).
To calculate the magnitude of a complex number in the form a+bi, we use the formula |z| = sqrt(a^2 + b^2). In this case, the magnitude of H(0.5 Hz) can be found by substituting the real and imaginary parts of H(0.5 Hz) into the formula: |H(0.5 Hz)| = sqrt(9.4^2 + (2π(0.5))^2).