Transform Theory - Study Mode
[#46] Laplace transform of the function sin ωt is
Correct Answer
(B) $$frac{omega }{{{{ ext{s}}^2} + {omega ^2}}}$$
[#47] For the function [{ ext{f}}left( { ext{x}}
ight) = left{ {x08egin{array}{*{20}{c}}
{ - 2,}&{ - pi < { ext{x}} < 0} \
{2,}&{0 < { ext{x}} < pi }
end{array}}
ight.] The value of a n in the Fourier series expansion of f(x) is
Correct Answer
(C) 0
[#48] Laplace transform of cos (ωt) is $$frac{{ ext{s}}}{{{{ ext{s}}^2} + {omega ^2}}}.$$ xa0The Laplace transform of e -2t cos(4t) is
Correct Answer
(D) $$frac{{{ ext{s}} + 2}}{{{{left( {{ ext{s}} + 2}
ight)}^2} + 16}}$$
[#49] The Laplace transform of sinh(at) is
Correct Answer
(C) $$frac{{ ext{a}}}{{{{ ext{s}}^2} - {{ ext{a}}^2}}}$$
[#50] The Fourier cosine series for an even function f(x) is given by $${ ext{f}}left( { ext{x}}
ight) = {{ ext{a}}_0} + sumlimits_{{ ext{n}} = 1}^infty {{{ ext{a}}_{ ext{n}}}cos left( {{ ext{nx}}}
ight)} $$ The value of the coefficient a 2 for the function f(x) = cos 2 (x) in [0, π] is
Correct Answer
(C) 0.5