Time Response – Verified PYQ Authority Guide
Time Responseis organised as a topic-level PYQ authority page. It brings together the strongest verified question clusters, exam/year coverage and concept-level practice so students can revise the topic without jumping through unrelated notes. Every factual learning cue below is drawn from the existing verified, published and approved English PYQ corpus or from its Knowledge Graph relationships; the hub does not invent unsupported technical claims.
PYQ evidence snapshot
4 verified PYQsare currently mapped to this Topic hub. The represented years include2026, 2025. Exam coverage currently includesDeputy Executive Engineer (Electrical), Class-2, Sports Authority of Gujarat / Assistant Engineer (Electrical), Class-2,, Assistant Engineer (Electrical), Class-2, Road and Building Department. Subject context includesElectrical Engineering. These values come from live mappings and can expand automatically when new verified PYQs are added.
Most useful verified PYQs to solve first
Start with the actual questions rather than memorising a generic note. The links below are ranked from the mapped corpus using repeat history and editorial quality, while the complete explanation stays on the individual question page.
- A second-order system has damping ratio 0.5 and natural frequency 4 rad/s, then 1. The system is underdamped and exhibits oscillatory response. 2. The damped natural frequency is less than the natural…
Deputy Executive Engineer (Electrical), Class-2, Sports Authority of Gujarat / Assistant Engineer (Electrical), Class-2, · 2026 · Damped Frequency Overshoot and Settling
Second-order dynamics are governed by two independent energy-storage states and are described by natural frequency and damping ratio. With ζ=0.5 and ωn=4 rad/s, ωd=ωn√(1−ζ²)≈3.46… - A first-order system has a time constant of 2 seconds and is subjected to a unit step input. The system gain is unity, then 1. The output reaches approximately 63 percent of…
Deputy Executive Engineer (Electrical), Class-2, Sports Authority of Gujarat / Assistant Engineer (Electrical), Class-2, · 2026 · Time Constant and Step Response
A standard first-order system has one real pole and an exponential step response controlled by a time constant τ. For τ=2 s, y(t)=1−e^(−t/2). At… - Consider the following statements regarding Second Order Systems: 1. Damping ratio determines the nature of system response such as overdamped, underdamped, or critically damped. 2. Underdamped systems show oscillatory response with decaying…
Deputy Executive Engineer (Electrical), Class-2, Sports Authority of Gujarat / Assistant Engineer (Electrical), Class-2, · 2026 · Damping Ratio and Response Type
Second-order dynamics are governed by two independent energy-storage states and are described by natural frequency and damping ratio. An underdamped response oscillates with exponentially… - What is the response of the feedback function with open loop transfer function G(s) = 4/s(s + 5) and input is input step?
Assistant Engineer (Electrical), Class-2, Road and Building Department · 2025 · Unity-Feedback Step Response
For unity feedback, first form T(s)=G(s)/(1+G(s)), then multiply by the step input 1/s and perform partial fractions. For G(s)=4/[s(s+5)], the closed-loop denominator is s²+5s+4=(s+1)(s+4),…
Formula & key-relationship bank from verified solutions
Characteristic form: s²+2ζω_n s+ω_n²=0.G(s)=1/(τs+1); y(t)=1−e^(−t/τ).T(s)=4/[s²+5s+4] =4/[(s+1)(s+4)] C(s)=T(s)/s =4/[s(s+1)(s+4)] c(t)=1−(4/3)e⁻ᵗ+(1/3)e⁻⁴ᵗ =1−(1/3)(4e⁻ᵗ−e⁻⁴ᵗ)
Use these as revision triggers and open the linked PYQ before applying a formula numerically; variable definitions and assumptions belong to the exact solved question.
Core ideas repeatedly reinforced by the solved corpus
- Second-order dynamics are governed by two independent energy-storage states and are described by natural frequency and damping ratio. With ζ=0.5 and ωn=4 rad/s, ωd=ωn√(1−ζ²)≈3.46 rad/s, so the response is underdamped and has nonzero overshoot. Key relation: Characteristic form:…
- A standard first-order system has one real pole and an exponential step response controlled by a time constant τ. For τ=2 s, y(t)=1−e^(−t/2). At t=2 s, y≈0.632. Key relation: G(s)=1/(τs+1); y(t)=1−e^(−t/τ). Exam focus: 63% at τ, ~95% at…
- Second-order dynamics are governed by two independent energy-storage states and are described by natural frequency and damping ratio. An underdamped response oscillates with exponentially decaying amplitude, critical damping gives the fastest non-oscillatory response, and overdamping gives a slower…
- For unity feedback, first form T(s)=G(s)/(1+G(s)), then multiply by the step input 1/s and perform partial fractions. For G(s)=4/[s(s+5)], the closed-loop denominator is s²+5s+4=(s+1)(s+4), giving the response 1−(1/3)(4e⁻ᵗ−e⁻⁴ᵗ).
Exam tips already validated in SRO solutions
- ζ1 overdamped.
- 63% at τ, ~95% at 3τ, ~99% at 5τ.
- Check c(0⁺)=0 and c(∞)=1 as quick validation.
Common mistakes to avoid
- Overdamped responses do not sustain oscillations.
- Do not confuse one time constant with 95% settling.
- Using open-loop G(s) directly as the step-response transfer function.
Topic and concept coverage
Mapped topic labels includeTime Response. The concept trail includesDamped Frequency Overshoot and Settling, Damping Ratio and Response Type, Time Constant and Step Response, Unity-Feedback Step Response. Use these labels as a revision map: move from the broad area to the narrow concept, solve a verified PYQ, inspect the detailed reasoning, and then attempt another question from the same cluster.
Knowledge Graph navigation
Continue withControl Systems,Closed-Loop Step Response,First-Order System,Second-Order System,Second-Order Systems,Electrical Engineering,Damped Frequency Overshoot and Settling,Damping Ratio and Response Type,Time Constant and Step Response,Unity-Feedback Step Response. These are canonical SRO entity links based on the Knowledge Graph and shared question mappings, not keyword-stuffed tag pages.
How to revise this authority page efficiently
- Solve before reading:answer a mapped PYQ first.
- Read the exact explanation:verify the correct principle, formula, distractor logic and common mistake on that question page.
- Move one level in the graph:use the closest concept/sub-topic/topic link rather than opening unrelated content.
- Reattempt:solve another verified PYQ from this hub and check whether the same error repeats.
Quality scope:this page is automatically maintained from SRO’s verified mapped corpus. It enriches one canonical authority URL instead of generating multiple near-duplicate pages for keyword variants. Manual authority articles are never overwritten by the automated engine.