A step change of magnitude is introduced to a system having the transfer function \[ G(s) = \frac{2}{s^2 + 2s + 4} \] The percent overshoot is:

Question

If the number of zeros is less than the number of poles, i.e. \( Z<P \), then the value of the transfer function becomes zero for \( s \to \infty \). Hence, some zeros are located at infinity and the order of such zeros will be:

Answer 1

Step 1: Determine the damping ratio.
The standard second-order system denominator is given by \( s^2 + 2 \zeta \omega_n s + \omega_n^2 \). From this, we identify \( \omega_n = 2 \) and \( 2 \zeta \omega_n = 2 \). Solving for the damping ratio \( \zeta \) yields \( \zeta = 0.5 \).

Step 2: Calculate the percent overshoot.
The formula for percent overshoot (PO) is: \[PO = e^{-\zeta \pi / \sqrt{1 - \zeta^2}} \times 100%\]With \( \zeta = 0.5 \) substituted into the formula: \[PO = e^{-0.5 \pi / \sqrt{0.75}} \times 100 \approx 16.3%.\]

Final Answer: \[\boxed{\text{C) 16.3}}\]

Firm 2	Cooperate	Compete
Firm 1	5, 5	0, 10
Compete	10,0	2, 2

A step change of magnitude is introduced to a system having the transfer function \[ G(s) = \frac{2}{s^2 + 2s + 4} \] The percent overshoot is:

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The Correct Option is C

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