GATE ECE 1998 | Continuous Time Signal Laplace Transform Question 23 | Signals and Systems

If L$$\left[ {f\left( t \right)} \right]$$ = $$\omega /\left( {{s^2} + {\omega ^2}} \right),$$ then the value of $$\matrix{ {Lim\,f\,\left( t \right)} \cr {t \to \infty } \cr } $$

cannot be determined

is zero

is unity

is infinite

GATE ECE 1997

MCQ (Single Correct Answer)

-0.3

The Laplace Transform of e_at .cos$$\left( {\alpha t} \right).u\left( t \right)$$ is equal to

$${{\left( {s - \alpha } \right)} \over {{{\left( {s - \alpha } \right)}^2} + {\alpha ^2}}}$$

$${{\left( {s + \alpha } \right)} \over {{{\left( {s + \alpha } \right)}^2} + {\alpha ^2}}}$$

$${1 \over {{{\left( {s - \alpha } \right)}^2}}}$$

none of the above

GATE ECE 1995

MCQ (Single Correct Answer)

-0.3

If L$$\left[ {f\left( t \right)} \right]$$ = $${{2\left( {s + 1} \right)} \over {{s^2} + 2s + 5}}$$, then $$f\left( {0 + } \right)\,$$ and $$f\left( \infty \right)$$ are given by

0, 2 respectively

2, 0 respectively

0, 1 respectively

2/5, 0 respectively

GATE ECE 1995

MCQ (Single Correct Answer)

-0.3

The final value theorem is used to find the

steady state value of the system output

initial value of the system output

transient behavior of the system output

none of these

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