Match the following lists : Correct codes are :List - I List - II a. Negative real and simple roots i. Sustained oscillatory b. Negative real and equal roots ii. Overdamped c. Complex conjugate roots iii. Critically damped d. Imaginary conjugate roots iv. Underdamped
a-ii, b-iii, c-iv, d-i
The question requires matching terms related to roots of a characteristic equation in control systems to their corresponding system behaviors.
- Negative real and simple roots: When a system has distinct negative real roots, it is referred to as an overdamped system. This means the system returns to equilibrium without oscillating, and the response is slower. Therefore,
a-ii. - Negative real and equal roots: This condition results in a critically damped system. The system returns to equilibrium as quickly as possible without oscillating. Thus,
b-iii. - Complex conjugate roots: These roots indicate an underdamped system. The system exhibits oscillations that gradually decay over time. Hence,
c-iv. - Imaginary conjugate roots: These roots suggest a sustained oscillatory system with no damping (purely oscillatory behavior). So,
d-i.
Thus, the correct matching of List-I to List-II is:
- a-ii: Negative real and simple roots - Overdamped
- b-iii: Negative real and equal roots - Critically damped
- c-iv: Complex conjugate roots - Underdamped
- d-i: Imaginary conjugate roots - Sustained oscillatory
Hence, the correct answer is: a-ii, b-iii, c-iv, d-i.
Similar Questions
The step, ramp and parabolic test input signals can respectively be expressed as
Assertion (A) : In control systems, steady state response in the final requirement for calculating the efficiency of the system.
Reason (R) : The transient response is also critical for the determination of the steady state response.
If the characteristic equation of a closed loop system is S2 + 2S + 2 = 0, then the system is
The open loop transfer function of a unity feedback control system is given by \(G(s)=\frac{25}{s(s+5)}\). The natural frequency of oscillator is fixed.
Arrange the damped frequency of oscillation for the following damping ratio in ascending order
A. \(\xi = 0.5\)
B. \(\xi = 0.1\)
C. \(\xi = 0.3\)
D. \(\xi = 0.25\)
E. \(\xi = 0.4\)
Choose the correct answer from the options given below :
The addition of a pole to the forward path transfer function of a closed loop system, generally has the effect of
consider a unity feedback control system for an open loop transfer function \(G(s)=\frac{5}{s(s+1)}\). Arrange the time constant in ascending order at different value of damping ratio of
A. \(\xi=3\)
B. \(\xi=7\)
C. \(\xi=1\)
D. \(\xi=10\)
E. \(\xi=5\)
Choose the correct answer from the options given below :
Important Questions from Time Response Analysis
Match the LIST-I with LIST-II
LIST-I
Transfer functionLIST-II
Step responseA. $\frac{25}{S^2+25}$ I. 
B. $\frac{36}{S^2+70S+36}$ II. 
C. $\frac{36}{S^2+12S+36}$ III. 
D. $\frac{36}{S^2+7S+49}$ IV. 
Choose the correct answer from the options given below:The step, ramp and parabolic test input signals can respectively be expressed as
Assertion (A) : In control systems, steady state response in the final requirement for calculating the efficiency of the system.
Reason (R) : The transient response is also critical for the determination of the steady state response.
If the characteristic equation of a closed loop system is S2 + 2S + 2 = 0, then the system is
The open loop transfer function of a unity feedback control system is given by \(G(s)=\frac{25}{s(s+5)}\). The natural frequency of oscillator is fixed.
Arrange the damped frequency of oscillation for the following damping ratio in ascending order
A. \(\xi = 0.5\)
B. \(\xi = 0.1\)
C. \(\xi = 0.3\)
D. \(\xi = 0.25\)
E. \(\xi = 0.4\)
Choose the correct answer from the options given below :
