Find the inverse Laplace transform of:
F(s)=2/s^4
L{1} = 1/s
L{t^n f(t)} = (-1)^n F(n)(s)
so, L{t^3} = 6/s^4
so,
f(t) = 1/3 t^3
To find the inverse Laplace transform of F(s), which is given as F(s) = 2/s^4, we can use the table of Laplace transforms or apply the properties of Laplace transforms.
The inverse Laplace transform of 1/s^n, where n is a positive integer, is given by:
L^-1 {1/s^n} = (n-1)! / t^n
In this case, n = 4. So, the inverse Laplace transform of 1/s^4 is:
L^-1 {1/s^4} = (4-1)! / t^4 = 3! / t^4 = 6 / t^4
Since F(s) = 2/s^4, we can multiply this result by 2:
L^-1 {F(s)} = 2 * L^-1 {1/s^4} = 2 * (6 / t^4) = 12 / t^4
Therefore, the inverse Laplace transform of F(s) = 2/s^4 is 12 / t^4.