Question:
The step response of a circuit is seen to have an oscillatory behaviour at the output with oscillations dying down after some time. The correct inference(s) regarding the transfer function from input to output is/are
The step response of a circuit is seen to have an oscillatory behaviour at the output with oscillations dying down after some time. The correct inference(s) regarding the transfer function from input to output is/are
Show Hint
For oscillatory behavior in a system's step response, the system must be of at least second order and have underdamped poles.
Updated On: Jan 8, 2026
- that it is of at least second order.
- that it has at least one pole-pair that is underdamped.
- that it does not have a real pole.
- that it is a first order system.
Hide Solution
Verified By Collegedunia
The Correct Option is A, B
Solution and Explanation
An oscillatory behavior with decaying oscillations in the step response indicates the presence of underdamped poles, which typically occur in systems of at least second order. Therefore, the correct answers are:
Step 1: Option (A) is correct because for oscillations to occur, the system must be of at least second order.
Step 2: Option (B) is correct because oscillations with decaying amplitude are a characteristic of underdamped poles, which are found in second order systems.
Step 3: Option (C) is incorrect because a system with oscillations must have at least one real or complex pole.
Step 4: Option (D) is incorrect because a first order system cannot exhibit oscillatory behavior.
Thus, the correct answers are (A) and (B).
Final Answer:
(A) that it is of at least second order, (B) that it has at least one pole-pair that is underdamped.
Was this answer helpful?
0
0
Top Questions on Transfer function
- The output \( y(t) \) of a first-order process is governed by the following differential equation: \[ \tau_p \frac{dy}{dt} + y = K_p f(t) \] where \( \tau_p \) is a non-zero time constant, \( K_p \) is the gain, and \( f(t) \) is the input with \( f(0) = 0 \). Assume \( y(0) = 0 \). The transfer function for this process is (consider \( s \) as the independent variable in the Laplace domain).
- GATE BT - 2025
- Genetics, Cellular and Molecular Biology
- Transfer function
- A thermometer measuring body temperature follows a first-order response with a time constant of 40 seconds. The instrument will reach 95% of its steady-state output at __ seconds.
- GATE BT - 2025
- Genetics, Cellular and Molecular Biology
- Transfer function
Consider the loop transfer function \(\frac {K(s+6)}{(s+3)(s+5)}\). In the root locus diagram the centroid will be located at:
- AP PGECET - 2024
- Instrumentation Engineering
- Transfer function
- The phase margin of the transfer function $G(s)=\dfrac{2(1-s)}{(1+s)^2}$ is ______ degrees (rounded off to the nearest integer).
- GATE IN - 2023
- Signals and Systems
- Transfer function
- A system has the transfer function $\dfrac{Y(s)}{X(s)}=\dfrac{s-\pi}{s+\pi}$. Let $u(t)$ be the unit–step function. The input $x(t)$ that results in a steady–state output $y(t)=\sin(\pi t)$ is _____.
- GATE IN - 2023
- Signals and Systems
- Transfer function
View More Questions
Questions Asked in GATE IN exam
- A car is moving collinearly with a laser beam emitted by a transceiver. A laser pulse emitted at \( t = 0 \) s is received back by the transceiver 100 ns (nanoseconds) later after reflection from the car. A second pulse emitted at \( t = 0.1 \) s is received back 90 ns later. Given the speed of light is \( 3 \times 10^8 \) m/s, the average speed of the car in this interval is _________
- GATE IN - 2022
- Displacement (linear and angular)
- Consider the function \( f(z) = \frac{1}{(z+1)(z+2)(z+3)} \). The residue of \( f(z) \) at \( z = -1 \) is _________.
- GATE IN - 2022
- Residue Theorem
- In the circuit shown, the load is driven by a sinusoidal ac voltage source \( V_1 = 100 \angle 0^\circ \, \text{V} \) at 50 Hz. Given \( R_1 = 20 \, \Omega \), \( C_1 = \left(\frac{1000}{\pi}\right) \, \mu\text{F} \), \( L_1 = \left(\frac{20}{\pi}\right) \, \text{mH} \), and \( R_2 = 4 \, \Omega \), the power factor is _________ (round off to one decimal place)
- GATE IN - 2022
- Transient analysis of RLC circuits with ac excitation
- In the circuit shown, the capacitance \( C_0 = 10 \, \mu\text{F} \) and inductance \( L_0 = 1 \, \text{mH} \) and the diode is ideal. The capacitor is initially charged to 10 V and the current in the inductor is initially zero. If the switch is closed at \( t = 0 \, \text{s} \), the voltage \( V_C(t) \) (in volts) across the capacitor at \( t = 0.5 \, \text{s} \) is _________ (round off to one decimal place)
- GATE IN - 2022
- Diodes: Characteristics and Applications
- In the circuit shown, the switch is initially closed. It is opened at \( t = 0 \, \text{s} \) and remains open thereafter. The time (in milliseconds) at which the output voltage \( V_{\text{out}} \) becomes LOW is _________ (round off to three decimal places).
- GATE IN - 2022
- Sample and hold circuits
View More Questions