GATE 2016 EE (EE2) – Question 60

A second-order real system has damping ratio 0.5, undamped natural frequency 10 rad/s and unit-step steady output 1.02. Its transfer function is

Show answer and explanation

Correct answer: (B) $102/(s^2+10s+100)$

Explanation

The standard denominator is s²+2ζωn s+ωn²=s²+10s+100. For a constant numerator N, DC gain is N/100.

The stated unit-step final value is the DC gain 1.02, requiring N=102. Thus the intended second-order form is **102/(s²+10s+100), B**.

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