What is the Laplace transform of impulse input having magnitude 'X'?
A. X
B. X2
C. $$\frac{{\text{1}}}{{\text{X}}}$$
D. 1
Answer: Option A
Solution (By Examveda Team)
The correct answer is A: X.Here's why:
An impulse function (also called a Dirac delta function) is a signal that is infinitely short and has an area of 1.
When the impulse has a magnitude of 'X', it means its area is 'X' instead of 1.
The Laplace transform is a mathematical tool used to convert time-domain functions (like signals) into the frequency domain.
A key property of the Laplace transform is that the Laplace transform of the unit impulse function (magnitude 1) is 1.
Since our impulse has a magnitude of 'X', we can think of it as 'X' times the unit impulse function.
The Laplace transform is a linear operator, meaning the Laplace transform of X * f(t) is X * F(s), where F(s) is the Laplace transform of f(t).
Therefore, the Laplace transform of an impulse with magnitude 'X' is X * 1 = X.
This Question Belongs to Chemical Engineering >> Process Control And Instrumentation
Join The Discussion
Comments (1)
Related Questions on Process Control and Instrumentation
Phase lag of the frequency response of a second order system to a sinusoidal forcing function
A. Is 30°
B. Is 90° at the most
C. Approaches 180° asymptotically
D. Is 120°
Which of the following is not classified as a thermo electric pyrometer?
A. Resistance thermometer
B. Thermocouple
C. Optical pyrometer (disappearing filament type)
D. Radiation pyrometer
A. Chromel-alumel
B. Iron-constantan
C. Platinum-platinum/rhodium
D. None of these
The correct answer is:
A. X
✅ Explanation:
An impulse input (also known as the Dirac delta function,
𝛿
(
𝑡
)
δ(t)) has a Laplace transform of:
𝐿
{
𝛿
(
𝑡
)
}
=
1
L{δ(t)}=1
Now, if the impulse has a magnitude
𝑋
X (i.e.,
𝑋
⋅
𝛿
(
𝑡
)
X⋅δ(t)), the Laplace transform becomes:
𝐿
{
𝑋
⋅
𝛿
(
𝑡
)
}
=
𝑋
⋅
𝐿
{
𝛿
(
𝑡
)
}
=
𝑋
⋅
1
=
𝑋
L{X⋅δ(t)}=X⋅L{δ(t)}=X⋅1=
X
✅ Final Answer:
A. X