UPSC Exam > UPSC Questions > Y(s)/U(s) =1/sL(1)=1/ssoY(t)=U(t) * 1but ther...
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Y(s)/U(s) =1/s
L(1)=1/s
so
Y(t)=U(t) * 1
but there mentioned
ans : Y(t)= U(t)* t
how t came instead of 1
please tell any one weather iam correct or not?
L(1)=1/s
so
Y(t)=U(t) * 1
but there mentioned
ans : Y(t)= U(t)* t
how t came instead of 1
please tell any one weather iam correct or not?
Most Upvoted Answer
Y(s)/U(s) =1/sL(1)=1/ssoY(t)=U(t) * 1but there mentioned ans : Y(t)= U...
Explanation:
Understanding the Transfer Function:
- The transfer function Y(s)/U(s) = 1/s represents a first-order system with a time constant of 1.
- When the Laplace transform of the unit step function U(t) is taken, it results in 1/s.
Deriving the Time-domain Response:
- To find the time-domain response Y(t), we need to take the inverse Laplace transform of the transfer function Y(s)/U(s).
- Multiplying U(t) by the inverse Laplace transform of 1/s results in the time-domain response Y(t) = U(t) * 1.
Interpreting the Result:
- The result Y(t) = U(t) * t is incorrect. The correct response should be Y(t) = U(t) * 1, as derived from the transfer function.
- The error in the mentioned answer might be due to a misunderstanding or miscalculation in the derivation process.
In conclusion, the correct time-domain response for the given transfer function is Y(t) = U(t) * 1, as per the properties of Laplace transforms and the transfer function provided.
Understanding the Transfer Function:
- The transfer function Y(s)/U(s) = 1/s represents a first-order system with a time constant of 1.
- When the Laplace transform of the unit step function U(t) is taken, it results in 1/s.
Deriving the Time-domain Response:
- To find the time-domain response Y(t), we need to take the inverse Laplace transform of the transfer function Y(s)/U(s).
- Multiplying U(t) by the inverse Laplace transform of 1/s results in the time-domain response Y(t) = U(t) * 1.
Interpreting the Result:
- The result Y(t) = U(t) * t is incorrect. The correct response should be Y(t) = U(t) * 1, as derived from the transfer function.
- The error in the mentioned answer might be due to a misunderstanding or miscalculation in the derivation process.
In conclusion, the correct time-domain response for the given transfer function is Y(t) = U(t) * 1, as per the properties of Laplace transforms and the transfer function provided.
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Y(s)/U(s) =1/sL(1)=1/ssoY(t)=U(t) * 1but there mentioned ans : Y(t)= U(t)* thow t came instead of 1please tell any one weather iam correct or not?
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