Transform Theory - Study Mode
[#11] A solution for the differential equation [{
m{dot x}}left( {
m{t}}
ight) + 2{
m{x}}left( {
m{t}}
ight) = delta left( {
m{t}}
ight)] xa0 xa0with initial condition x(0 - ) = 0 is
Correct Answer
(A) e -2t u(t)
[#12] Consider the differential equation $$frac{{{{ ext{d}}^2}{ ext{y}}left( { ext{t}}
ight)}}{{{ ext{d}}{{ ext{t}}^2}}} + 2frac{{{ ext{dy}}left( { ext{t}}
ight)}}{{{ ext{dt}}}} + { ext{y}}left( { ext{t}}
ight) = delta left( { ext{t}}
ight)$$ xa0 xa0 xa0with $${left. {{ ext{y}}left( { ext{t}}
ight)}
ight|_{{ ext{t}} = 0}} = - 2$$ xa0 and $${left. {frac{{{ ext{dy}}}}{{{ ext{dt}}}}}
ight|_{{ ext{t}} = 0}} = 0.$$ The numerical value of $${left. {frac{{{ ext{dy}}}}{{{ ext{dt}}}}}
ight|_{{ ext{t}} = 0}}$$ xa0 is
Correct Answer
(D) 1
[#13] A delayed unit step function is defined as [{ ext{u}}left( {{ ext{t}} - { ext{a}}}
ight) = left{ {x08egin{array}{*{20}{c}}
{0,}&{{ ext{for t}} < { ext{a}}} \
{1,}&{{ ext{for t}} geqslant { ext{a}}}
end{array}}
ight..] xa0 xa0 xa0Its Laplace transform is
Correct Answer
(D) $$frac{{{{ ext{e}}^{{ ext{as}}}}}}{{ ext{a}}}$$
[#14] The Laplace Transform of f(t) = e 2t sin(5t) u(t) is
Correct Answer
(A) $$frac{5}{{{{ ext{s}}^2} - 4{ ext{s}} + 29}}$$
[#15] Let $${ ext{X}}left( { ext{s}}
ight) = frac{{3{ ext{s}} + 5}}{{{{ ext{s}}^2} + 10{ ext{s}} + 21}}$$ xa0 xa0be the Laplace Transform of a signal x(t). Then, x(0 + ) is
Correct Answer
(B) 3