Time Response MCQs

Practice Time Response MCQs with four options, answers and explanations for focused Electronics & Telecommunication Engineering revision.

Question 1

Control SystemsTime Response

For a first-order system with time constant T, the unit-step response reaches approximately 63.2% of its final value at?

At=T
Bt=2T
Ct=5T
Dt=T/10

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Correct Answer: A. t=T

Explanation: The normalized first-order step response is 1-e^(-t/T); at t=T it equals 1-e^-1≈0.632.

Reference: Standard control systems: time response

Question 2

Control SystemsTime Response

A first-order system is commonly considered essentially settled to within about 2% after approximately?

AT
B2T
C4T
D10T

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Correct Answer: C. 4T

Explanation: For a standard first-order response, e^-4≈0.0183, so about 4 time constants corresponds to the 2% settling criterion.

Reference: Standard control systems: time response

Question 3

Control SystemsTime Response

A first-order system has transfer function 1/(Ts+1). The parameter T represents its?

ATime constant
BDamping ratio
CNatural frequency
DSteady-state gain only

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Correct Answer: A. Time constant

Explanation: T is the first-order time constant and determines how quickly the exponential transient decays.

Reference: Standard control systems: time response

Question 4

Control SystemsTime Response

For a stable underdamped second-order system, increasing damping ratio generally causes percentage overshoot to?

AIncrease
BDecrease
CRemain exactly unchanged
DBecome infinite

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Correct Answer: B. Decrease

Explanation: For 0<ζ<1, greater damping ratio generally reduces percentage overshoot.

Reference: Standard control systems: time response

Question 5

Control SystemsTime Response

For a standard underdamped second-order system, the peak time Tp is?

Aπ/ωn
Bπ/[ωn√(1-ζ²)]
C4/(ζωn)
D1/(ζωn)

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Correct Answer: B. π/[ωn√(1-ζ²)]

Explanation: For 0<ζ<1, the damped natural frequency is ωd=ωn√(1-ζ²), and peak time Tp=π/ωd.

Reference: Standard control systems: time response

Question 6

Control SystemsTime Response

A standard second-order system has ζ=0.6 and ωn=5 rad/s. Its damped natural frequency ωd is?

A2 rad/s
B3 rad/s
C4 rad/s
D5 rad/s

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Correct Answer: C. 4 rad/s

Explanation: ωd=ωn√(1-ζ²)=5√(1-0.36)=5×0.8=4 rad/s.

Reference: Standard control systems: time response

Question 7

Control SystemsTime Response

For ζ=0.6 and ωn=5 rad/s, the peak time is approximately?

A0.314 s
B0.628 s
C0.785 s
D1.571 s

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Correct Answer: C. 0.785 s

Explanation: ωd=4 rad/s, so Tp=π/4≈0.785 s.

Reference: Standard control systems: time response

Question 8

Control SystemsTime Response

Using the common 2% criterion, the settling time of a standard underdamped second-order system is approximately?

A1/(ζωn)
B2/(ζωn)
C4/(ζωn)
Dπ/(ζωn)

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Correct Answer: C. 4/(ζωn)

Explanation: For the 2% settling band, Ts≈4/(ζωn) is a widely used approximation.

Reference: Standard control systems: time response

Question 9

Control SystemsTime Response

For ζ=0.5 and ωn=10 rad/s, the approximate 2% settling time is?

A0.2 s
B0.4 s
C0.8 s
D2 s

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Correct Answer: C. 0.8 s

Explanation: Ts≈4/(ζωn)=4/(0.5×10)=0.8 s.

Reference: Standard control systems: time response

Question 10

Control SystemsTime Response

For a standard underdamped second-order system, percentage overshoot is given by?

A100e^[-πζ/√(1-ζ²)]
B100ζωn
C100/(1+ζ)
D100e^(-ωn)

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Correct Answer: A. 100e^[-πζ/√(1-ζ²)]

Explanation: The standard step-response percentage overshoot is PO=100 exp[-πζ/√(1-ζ²)] for 0<ζ<1.

Reference: Standard control systems: time response

Question 11

Control SystemsTime Response

For ζ=1/√2≈0.707, the percentage overshoot of a standard second-order step response is closest to?

A0%
B4.3%
C16.3%
D50%

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Correct Answer: B. 4.3%

Explanation: Substituting ζ≈0.707 in the overshoot formula gives approximately 4.3%.

Reference: Standard control systems: time response