Find the inverse Laplace transform of:
F(s)=3/(s-4)
just check your tables.
L{1} = 1/s
L{e^at f(t) = F(s-a)
so,
L{3e^4t} = 3/(s-4)
To find the inverse Laplace transform of F(s), we can use the following steps:
1. Start with the given Laplace transform F(s).
F(s) = 3/(s - 4)
2. Identify the corresponding function in the time domain.
We are looking for f(t), the inverse Laplace transform of F(s).
3. Use a partial fraction decomposition to express F(s) in a form that can be easily inverted.
F(s) = 3/(s - 4)
= A/(s - 4) [Assume A as the unknown constant]
To find A, we can multiply both sides of the equation by (s - 4) and then substitute s = 4.
3 = A
A = 3
Therefore, F(s) = 3/(s - 4) can be written as:
F(s) = 3/(s - 4) = 3/(s - 4)
4. Apply the inverse Laplace transform to each term.
f(t) = A * e^(at)
In this case, A = 3 and a = 4.
f(t) = 3 * e^(4t)
Therefore, the inverse Laplace transform of F(s) is f(t) = 3 * e^(4t).