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The output response of a system is denoted as y(t), and its Laplace transform is given by
10
Y(s) = s(s 2 +s+100√2) .
The steady state value of y(t) is?
10
Y(s) = s(s 2 +s+100√2) .
The steady state value of y(t) is?
Most Upvoted Answer
The output response of a system is denoted as y(t), and its Laplace tr...
Steady State Value of y(t)
To find the steady state value of y(t), we need to determine the value of y(t) as t approaches infinity. In the Laplace domain, the steady state value corresponds to the value of Y(s) as s approaches zero.
Given Information:
The Laplace transform of the system's output, Y(s), is given by:
10Y(s) = s(s^2 - s + 100√2)
Step 1: Simplify the Laplace transform expression:
To find the steady state value of y(t), we need to solve for Y(s). Let's simplify the given expression:
10Y(s) = s(s^2 - s + 100√2)
Step 2: Solve for Y(s):
Divide both sides of the equation by 10:
Y(s) = (s(s^2 - s + 100√2))/10
Step 3: Take the limit as s approaches zero:
To find the steady state value, we need to evaluate Y(s) as s approaches zero:
lim(s→0) Y(s) = lim(s→0) (s(s^2 - s + 100√2))/10
Step 4: Evaluate the limit:
Let's evaluate the limit using algebraic simplification:
lim(s→0) (s(s^2 - s + 100√2))/10
= (0(0^2 - 0 + 100√2))/10
= 0
Step 5: Interpretation:
The steady state value of y(t) is 0. This means that as time approaches infinity, the output of the system settles at zero. In other words, the system reaches a steady state where the output remains constant at zero.
Summary:
The steady state value of y(t) for the given system is 0. This indicates that the output of the system settles at zero as time approaches infinity.
To find the steady state value of y(t), we need to determine the value of y(t) as t approaches infinity. In the Laplace domain, the steady state value corresponds to the value of Y(s) as s approaches zero.
Given Information:
The Laplace transform of the system's output, Y(s), is given by:
10Y(s) = s(s^2 - s + 100√2)
Step 1: Simplify the Laplace transform expression:
To find the steady state value of y(t), we need to solve for Y(s). Let's simplify the given expression:
10Y(s) = s(s^2 - s + 100√2)
Step 2: Solve for Y(s):
Divide both sides of the equation by 10:
Y(s) = (s(s^2 - s + 100√2))/10
Step 3: Take the limit as s approaches zero:
To find the steady state value, we need to evaluate Y(s) as s approaches zero:
lim(s→0) Y(s) = lim(s→0) (s(s^2 - s + 100√2))/10
Step 4: Evaluate the limit:
Let's evaluate the limit using algebraic simplification:
lim(s→0) (s(s^2 - s + 100√2))/10
= (0(0^2 - 0 + 100√2))/10
= 0
Step 5: Interpretation:
The steady state value of y(t) is 0. This means that as time approaches infinity, the output of the system settles at zero. In other words, the system reaches a steady state where the output remains constant at zero.
Summary:
The steady state value of y(t) for the given system is 0. This indicates that the output of the system settles at zero as time approaches infinity.
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The output response of a system is denoted as y(t), and its Laplace transform is given by10Y(s) = s(s 2 +s+100√2) .The steady state value of y(t) is?
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The output response of a system is denoted as y(t), and its Laplace transform is given by10Y(s) = s(s 2 +s+100√2) .The steady state value of y(t) is? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The output response of a system is denoted as y(t), and its Laplace transform is given by10Y(s) = s(s 2 +s+100√2) .The steady state value of y(t) is? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The output response of a system is denoted as y(t), and its Laplace transform is given by10Y(s) = s(s 2 +s+100√2) .The steady state value of y(t) is?.
The output response of a system is denoted as y(t), and its Laplace transform is given by10Y(s) = s(s 2 +s+100√2) .The steady state value of y(t) is? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The output response of a system is denoted as y(t), and its Laplace transform is given by10Y(s) = s(s 2 +s+100√2) .The steady state value of y(t) is? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The output response of a system is denoted as y(t), and its Laplace transform is given by10Y(s) = s(s 2 +s+100√2) .The steady state value of y(t) is?.
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