Question

MCQ (100)
Q48.
Consider system with transfer function G(S)
(3+6)/Ks?+s+6. Its damping ratio will be 0.5 when the values of
k is:
​

Answer 1

Answer:

Options C is correct........

Answer 2

Ques. Consider a system with transfer function G(s) = s+6/Ks2+s+6. Its damping ratio will be 0.5 when the values of k is:

a)2/6

b)3

c)1/6

d)6

Answer:

The correct answer is option c) $\frac{1}{6}$.

Step-by-step explanation:

Concept:

The parameter is known as the damping ratio, and the parameter is known as the natural frequency. The oscillations' rate of decay between each bounce is measured by the damping ratio. It is represented by $\zeta$ (zeta). A transfer function is a mathematical association between a numerical input to a dynamic system and the produced output in statistical time-series analysis, signal processing, and control engineering.

Given:

$G(s) = \frac{s+6}{Ks^{2} +s+6}$

The damping ratio will be $=0.5$

To find:

We have to find the value of $k$.

Solution:

Follow the steps given below:

$\frac{ s+6}{K[s^{2}+\frac{s}{k}+\frac{6}{k} ] }$ Comparing with $s^{2}+2Gw+w^{2}$

$w= \frac{\sqrt{6}}{k}$

$2Gw=\frac{1}{k}$

$2*0.5*\frac{\sqrt{6}}{k} =\frac{1}{k}$

$k=\frac{1}{6}$

Thus, the required value of $k$ is $\frac{1}{6}$.

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