Test: Laplace Transform- 1
10 Questions MCQ Test Signals and Systems | Test: Laplace Transform- 1
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Determine the Laplace transform of given signal.
Q. x(t) = u( t - 2)
Q. x(t) = u( t - 2)
We know that,
Here, f(t) = sin(2t) => F(s) =
Hence, L(t2sin(2t)) =
Determine the Laplace transform of given signal.
Q. x(t) = e-2tu(t+1)
Q. x(t) = e-2tu(t+1)
Laplace transform e-at u(t) = 1/s+a
for all Re(s) > - Re(a)
e-2t u(t+1) = 1/(s+2)
Determine the Laplace transform of given signal.
Q. x(t) = e2tu(-t+2)
Determine the Laplace transform of given signal.
Q. x(t) = sin 5 t
Determine the Laplace transform of given signal.
Q. x( t) = u(t) - u(t - 2)
Determine the Laplace transform of given signal.
Q. x( t) = d/dt {te-1u(t)}
Determine the Laplace transform of given signal.
Q. x( t) = tu(t)*cos2πt u(t)
Determine the Laplace transform of given signal.
Q. x( t) = t3u(t)
Determine the Laplace transform of given signal.
Q. x(t) = u( t - 1) * e-2tu( t - 1)
L{−e-at u(t)}
= ∫(∞ to −∞) −e-at u(t)e-stdt
L{−e-at u(t)}
= ∫(∞ to 0) − e-(s+a)t dt
= - |e-(s+a)t/−(s+a)|∞ to 0
= −1/s+a
=> L{−e-2t u(t)} = -1/s+2
=> L{−e-2t u(t-1)} = e-(s+2)/s2 …………(1)
q(t) = L{u(t-1)}
= e-s/(s2)................(2)
Multiply (1) and (2)
= e-2(s+1)/(s+2)
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