Transform Theory - Study Mode

[#26] Find the inverse Laplace transform of $$Fleft( s
ight) = frac{{{s^2} + 2s - 2}}{{sleft( {s + 4}
ight)left( {s - 5}
ight)}}$$
Correct Answer

(A) $$left( {frac{1}{{10}} + frac{1}{6}{e^{ - 4t}} + frac{{11}}{{15}}{e^{5t}}} ight)uleft( t ight)$$

[#27] Give transfer function $$Hleft( s
ight) = frac{{s + 2}}{{{s^2} + s + 4}},$$ xa0 xa0under steady state condition, the sinusoidal input and output are, respectively x(t) = cos 2t, y(t) = cos(2t + $$phi $$), then angle $$phi $$ will be
Correct Answer

(C) -45°

[#28] Which of the following correctly defines Laplace transform of a function in the time domain?
Correct Answer

(A) $$Lleft{ {fleft( t ight)} ight} = int_{{0^ - }}^infty {fleft( t ight){e^{ - st}}dt} $$

[#29] The Laplace transform of $$Ileft( t
ight)$$ xa0is given by $$Ileft( s
ight) = frac{5}{{sleft( {{s^2} + 2}
ight)}}.$$ xa0 xa0As $$t o infty $$ xa0the value of $$Ileft( t
ight)$$ xa0tends to
Correct Answer

(C) $$frac{5}{2}$$

[#30] Given that $$Fleft( s
ight)$$ xa0is the one-side Laplace transform of $$fleft( t
ight),$$ xa0the Laplace transform of $$int_0^t {fleft( au
ight)d au } $$ xa0 is
Correct Answer

(B) $$frac{1}{s}Fleft( s ight)$$