1
GATE ECE 2006
+1
-0.3
Consider the function $$f(t)$$ having laplace transform
$$F\left( s \right) = {{{\omega _0}} \over {{s^2} + \omega _0^2}},\,\,{\mathop{\rm Re}\nolimits} \left( s \right) > 0.$$ The final value of $$f(t)$$ would be ____________.
A
$$0$$
B
$$1$$
C
$$- 1 - f\left( \infty \right) \le 1$$
D
$$\infty$$
2
GATE ECE 2005
+1
-0.3
In what range should $$Re(s)$$ remain so that the laplace transform of the function $${e^{\left( {a + 2} \right)t + 5}}$$ exists?
A
$${\mathop{\rm Re}\nolimits} \left( s \right) > a + 2$$
B
$${\mathop{\rm Re}\nolimits} \left( s \right) > a + 7$$
C
$${\mathop{\rm Re}\nolimits} \left( s \right) < 2$$
D
$${\mathop{\rm Re}\nolimits} \left( s \right) > a + 5$$
3
GATE ECE 2003
+1
-0.3
The laplace transform of $$i(t)$$ is given by
$$I\left( s \right) = {2 \over {s\left( {1 + s} \right)}}$$ As $$t \to \infty ,$$ the value of $$i(t)$$ tends to __________.
A
$$0$$
B
$$1$$
C
$$2$$
D
$$\infty$$
4
GATE ECE 1999
+1
-0.3
If $$\,\,L\left\{ {f\left( t \right)} \right\} = F\left( s \right)$$ then $$\,\,\,L\left\{ {f\left( {t - T} \right)} \right\}$$ is equal to
A
$${e^{s\,T}}F\left( s \right)$$
B
$${e^{ - s\,T}}F\left( s \right)$$
C
$${{F\left( s \right)} \over {1 - {e^{s\,T}}}}$$
D
$${{F\left( s \right)} \over {1 - {e^{ - s\,T}}}}$$
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