Transform Theory - Study Mode
[#1] Laplace transform of sin ht is
Correct Answer
(A) $$frac{1}{{{{ ext{S}}^2} - 1}}$$
[#2] Laplace transform of cos (ωt) is
Correct Answer
(A) $$frac{{ ext{s}}}{{{{ ext{s}}^2} + {omega ^2}}}$$
[#3] The Laplace transform of a function f(t) is $$frac{1}{{{{ ext{s}}^2}left( {{ ext{s}} + 1}
ight)}}.$$ xa0The function f(t) is
Correct Answer
(A) t - 1 + e -1
[#4] The inverse Laplace transform of $${ ext{H}}left( { ext{s}}
ight) = frac{{{ ext{s}} + 3}}{{{{ ext{s}}^2} + 2{ ext{s}} + 1}}$$ xa0 xa0for t ≥ 0 is
Correct Answer
(A) 2t e -t + e -t
[#5] Let [{ ext{f}}left( { ext{x}}
ight) = left{ {x08egin{array}{*{20}{c}}
{ - pi ,,,{ ext{if}}}&{ - pi < { ext{x}} leqslant { ext{0}}} \
{pi ,,,{ ext{if}}}&{0 < { ext{x}} leqslant pi }
end{array}}
ight.] xa0 xa0 be a periodic function of period 2π. The coefficient of sin5x in the Fourier series expansion of f(x) in the interval [-π, π] is
Correct Answer
(A) $$frac{4}{5}$$