Question

For a first-order system, \(H(s)=\dfrac{1}{s+1}\). The magnitude of the frequency response at \(\omega=0\) is

• A. \(0\)
• B. \(0.5\)
• C. \(1\)
• D. \(\infty\)

Hint:

For \[ H(s)=\frac{1}{s+a}, \] the magnitude response is \[ \boxed{ |H(j\omega)| = \frac{1}{\sqrt{a^2+\omega^2}}. } \] At \(\omega=0\), \[ \boxed{|H(0)|=\frac1a.} \]

Answer 1

The Correct Option is C

Step 1: Obtain the frequency response. Substitute \[ s=j\omega \] into the transfer function: \[ H(j\omega) = \frac{1}{1+j\omega}. \]

Step 2: Evaluate the magnitude at \(\omega=0\). At \[ \omega=0, \] \[ H(j0) = \frac{1}{1+j0} = 1. \] Hence, \[ |H(j0)| = 1. \] Therefore, \[ \boxed{(C)} \] is the correct answer.