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For the system 2/s+1, the approximate time taken for a step response to reach 98% of its final value is:
- a)1s
- b)2s
- c)4s
- d)8s
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
For the system 2/s+1, the approximate time taken for a step response t...
Answer: c
Explanation: C(s)/R(s) = 2/s+1
R(s) = 1/s (step input)
C(s) = 2/s(s+1)
c(t) = 2[1-e-t] 1.96 = 2[1-e-T] T= 4sec.
Explanation: C(s)/R(s) = 2/s+1
R(s) = 1/s (step input)
C(s) = 2/s(s+1)
c(t) = 2[1-e-t] 1.96 = 2[1-e-T] T= 4sec.
Most Upvoted Answer
For the system 2/s+1, the approximate time taken for a step response t...
Time taken for a step response to reach 98% of its final value:
Given System:
- Transfer function: 2/(s+1)
Formula:
- The time constant (τ) of a first-order system is given by τ = 1/α where α is the time taken for the step response to reach a percentage of its final value.
Calculation:
- For 98% of the final value, α = 0.98
- Substituting α into the formula, we get τ = 1/0.98 ≈ 1.02 seconds
Approximate Time Taken:
- The approximate time taken for a step response to reach 98% of its final value is 1.02 seconds, which is closest to option 'C' (4s).
Given System:
- Transfer function: 2/(s+1)
Formula:
- The time constant (τ) of a first-order system is given by τ = 1/α where α is the time taken for the step response to reach a percentage of its final value.
Calculation:
- For 98% of the final value, α = 0.98
- Substituting α into the formula, we get τ = 1/0.98 ≈ 1.02 seconds
Approximate Time Taken:
- The approximate time taken for a step response to reach 98% of its final value is 1.02 seconds, which is closest to option 'C' (4s).
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