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Determine the Laplace transform of given signal.
Q. x( t) = t3u(t)
Q. x( t) = t3u(t)
- a)3/s4
- b)-3/s4
- c)6/s4
- d)-6/s4
Correct answer is option 'C'. Can you explain this answer?
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Determine the Laplace transform of given signal.Q.x( t) = t3u(t)a)3/s4...
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Determine the Laplace transform of given signal.Q.x( t) = t3u(t)a)3/s4...
Understanding the Laplace Transform
The Laplace transform is a powerful tool in engineering used to analyze linear time-invariant systems. It transforms a time-domain function into a complex frequency domain representation.
Given Signal
The signal provided is x(t) = t^3 * u(t), where u(t) is the unit step function. The unit step function ensures that x(t) is zero for t < 0.="" />Laplace Transform Formula
The Laplace transform of a function f(t) is defined as:
- L{f(t)} = ∫(from 0 to ∞) e^(-st) * f(t) dt
For x(t) = t^3 * u(t), we apply the formula:
- L{t^n} = n! / s^(n+1)
where n corresponds to the power of t.
Calculating the Transform
For our case: n = 3
- L{t^3} = 3! / s^(3+1)
Calculating 3!:
- 3! = 6
Thus,
- L{t^3} = 6 / s^4
Conclusion
The Laplace transform of the signal x(t) = t^3 * u(t) is:
- L{x(t)} = 6 / s^4
This matches option 'C', confirming that the correct answer is indeed 6/s^4. The Laplace transform simplifies the analysis of systems and signals, making it an essential aspect of electrical engineering.
The Laplace transform is a powerful tool in engineering used to analyze linear time-invariant systems. It transforms a time-domain function into a complex frequency domain representation.
Given Signal
The signal provided is x(t) = t^3 * u(t), where u(t) is the unit step function. The unit step function ensures that x(t) is zero for t < 0.="" />Laplace Transform Formula
The Laplace transform of a function f(t) is defined as:
- L{f(t)} = ∫(from 0 to ∞) e^(-st) * f(t) dt
For x(t) = t^3 * u(t), we apply the formula:
- L{t^n} = n! / s^(n+1)
where n corresponds to the power of t.
Calculating the Transform
For our case: n = 3
- L{t^3} = 3! / s^(3+1)
Calculating 3!:
- 3! = 6
Thus,
- L{t^3} = 6 / s^4
Conclusion
The Laplace transform of the signal x(t) = t^3 * u(t) is:
- L{x(t)} = 6 / s^4
This matches option 'C', confirming that the correct answer is indeed 6/s^4. The Laplace transform simplifies the analysis of systems and signals, making it an essential aspect of electrical engineering.
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Determine the Laplace transform of given signal.Q.x( t) = t3u(t)a)3/s4b)-3/s4c)6/s4d)-6/s4Correct answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Determine the Laplace transform of given signal.Q.x( t) = t3u(t)a)3/s4b)-3/s4c)6/s4d)-6/s4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine the Laplace transform of given signal.Q.x( t) = t3u(t)a)3/s4b)-3/s4c)6/s4d)-6/s4Correct answer is option 'C'. Can you explain this answer?.
Determine the Laplace transform of given signal.Q.x( t) = t3u(t)a)3/s4b)-3/s4c)6/s4d)-6/s4Correct answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Determine the Laplace transform of given signal.Q.x( t) = t3u(t)a)3/s4b)-3/s4c)6/s4d)-6/s4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine the Laplace transform of given signal.Q.x( t) = t3u(t)a)3/s4b)-3/s4c)6/s4d)-6/s4Correct answer is option 'C'. Can you explain this answer?.
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