Inverse Laplace Transformations - One Line Questions
1.
What is the inverse Laplace transform of F(s) = 1 / (s(s+a))? —
(1 - e^(-at)) / a
2.
What is the inverse Laplace transform of F(s) = 1 / (s(s-a))? —
(1 - e^(at)) / a
3.
What is the inverse Laplace transform of F(s) = 1 / ((s-a)(s²+a²))? —
(e^(at) - cos(at)) / a²
4.
What is the inverse Laplace transform of F(s) = 1/(s-a)(s-b), where a ≠ b? —
(e^(at) - e^(bt)) / (a-b)
5.
What is the inverse Laplace transform of F(s) = 1 / (s-a)(s-b), where a ≠ b? —
(e^(at) - e^(bt)) / (a-b)
6.
What is the inverse Laplace transform of F(s) = 1/(s+a)ⁿ, where n is a positive integer? —
(t^(n-1) * e^(-at)) / (n-1)!
7.
What is the inverse Laplace transform of F(s) = 1 / (s+a)ⁿ, where n is a positive integer? —
(t^(n-1) * e^(-at)) / (n-1)!
8.
What is the inverse Laplace transform of F(s) = 1/(s-a)ⁿ, where n is a positive integer? —
(t^(n-1) * e^(at)) / (n-1)!
9.
What is the inverse Laplace transform of F(s) = 1 / (s-a)ⁿ, where n is a positive integer? —
(t^(n-1) * e^(at)) / (n-1)!
10.
Using partial fraction decomposition, find the inverse Laplace transform of F(s) = 1 / (s(s+1)). —
1 - e^(-t)
11.
What is the inverse Laplace transform of F(s) = s / ((s-1)(s-2))? —
2e^(2t) - e^t
12.
If F(s) = s/(s² + a²), what is its inverse Laplace transform? —
cos(at)
13.
What is the inverse Laplace transform of F(s) = s / (s² + a²)? —
cos(at)
14.
If F(s) = s/(s² - a²), what is its inverse Laplace transform? —
cosh(at)
15.
What is the inverse Laplace transform of F(s) = s / (s² - a²)? —
cosh(at)
16.
What is the inverse Laplace transform of F(s) = 1 / (s² + 4s + 5)? —
e^(-2t) * sin(t)
17.
What is the inverse Laplace transform of F(s) = 1 / (s² + 6s + 10)? —
e^(-3t) * sin(t)
18.
What is the inverse Laplace transform of F(s) = 1/(s² + 2s + 5)? —
e^(-t) * sin(2t) / 2
19.
What is the inverse Laplace transform of F(s) = 1 / (s² + 2s + 2)? —
e^(-t) * sin(t)
20.
What is the inverse Laplace transform of F(s) = 1 / (s² - 4s + 5)? —
e^(2t) * sin(t)
21.
What is the inverse Laplace transform of F(s) = 1 / (s² - 6s + 10)? —
e^(3t) * sin(t)
22.
If F(s) = 1/(s-a), what is its inverse Laplace transform? —
e^(at)
23.
What is the inverse Laplace transform of F(s) = 1/(s² - 2s + 5)? —
e^t * sin(2t) / 2
24.
What is the inverse Laplace transform of F(s) = 1 / (s² - 2s + 2)? —
e^t * sin(t)
25.
What is the inverse Laplace transform of F(s) = a/(s² + a²)? —
sin(at)
26.
What is the inverse Laplace transform of F(s) = 1 / (s² + a²)? —
sin(at) / a
27.
What is the inverse Laplace transform of F(s) = 1/(s² + a²)? —
sin(at)/a
28.
What is the inverse Laplace transform of F(s) = a/(s² - a²)? —
sinh(at)
29.
What is the inverse Laplace transform of F(s) = 1 / (s² - a²)? —
sinh(at) / a
30.
What is the inverse Laplace transform of F(s) = 1/(s² - a²)? —
sinh(at)/a
31.
What is the inverse Laplace transform of F(s) = 1/s²? —
t
32.
Find the inverse Laplace transform of F(s) = 1 / (s²(s+1)). —
t - 1 + e^(-t)
33.
What is the inverse Laplace transform of F(s) = 1 / (s² + 4s + 4)? —
t * e^(-2t)
34.
What is the inverse Laplace transform of F(s) = 1/(s+a)²? —
t * e^(-at)
35.
What is the inverse Laplace transform of F(s) = 1/(s+a)²? —
t * e^(-at)
36.
What is the inverse Laplace transform of F(s) = 1 / (s+a)²? —
t * e^(-at)
37.
What is the inverse Laplace transform of F(s) = 1 / (s² + 2s + 1)? —
t * e^(-t)
38.
What is the inverse Laplace transform of F(s) = 1 / (s² - 4s + 4)? —
t * e^(2t)
39.
What is the inverse Laplace transform of F(s) = 1/(s-a)²? —
t * e^(at)
40.
What is the inverse Laplace transform of F(s) = 1/(s-a)²? —
t * e^(at)
41.
What is the inverse Laplace transform of F(s) = 1 / (s-a)²? —
t * e^(at)
42.
What is the inverse Laplace transform of F(s) = 1 / (s² - 2s + 1)? —
t * e^t
43.
Find the inverse Laplace transform of F(s) = n! / s^(n+1). —
t^n
44.
What is the inverse Laplace transform of F(s) = 1/(s+a)³? —
t² * e^(-at) / 2
45.
What is the inverse Laplace transform of F(s) = 1 / (s+a)³? —
t² * e^(-at) / 2
46.
What is the inverse Laplace transform of F(s) = 1/(s-a)³? —
t² * e^(at) / 2
47.
What is the inverse Laplace transform of F(s) = 1 / (s-a)³? —
t² * e^(at) / 2
48.
What is the definition of the inverse Laplace transform of a function F(s)? —
The function f(t) such that L{f(t)} = F(s)
49.
Which property of inverse Laplace transforms states that L⁻¹{aF(s) + bG(s)} = aL⁻¹{F(s)} + bL⁻¹{G(s)}? —
Linearity Property
50.
What is the inverse Laplace transform of F(s) = 1/(s+a)ⁿ⁺¹, where n is a non-negative integer? —
tⁿ * e^(-at) / n!