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A second-order real system has the following properties:

a) the damping ratio $\zeta=0.5$ and undamped natural frequency $\omega _{n}=10$ rad/s

b) the steady state value of the output, to a unit step input, is $1.02$.

The transfer function of the system is

  1. $\frac{1.02}{s^{2}+5s+100}$
  2. $\frac{102}{s^{2}+10s+100}$
  3. $\frac{100}{s^{2}+10s+100}$
  4. $\frac{102}{s^{2}+5s+100}$
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