The inverse Laplace transform is used to revert a function from the frequency domain (s) back to the time domain (t).

Given the function F(s) = -3e^(-5s), we can see that it is a shifted function.

The inverse Laplace transform of a shifted function is given by L^(-1){e^(-as)F(s)} = u(t-a)f(t-a), where u(t-a) is the unit step function.

In this case, a = 5 and F(s) = -3.

The inverse Laplace transform of F(s) = -3 is simply -3δ(t), where δ(t) is the Dirac delta function.

Therefore, the inverse Laplace transform of F(s) = -3e^(-5s) is -3u(t-5)δ(t-5).

This means that the function is 0 for t

Question

The inverse Laplace transform is used to revert a function from the frequency domain (s) back to the time domain (t).

Given the function F(s) = -3e^(-5s), we can see that it is a shifted function.

The inverse Laplace transform of a shifted function is given by L^(-1){e^(-as)F(s)} = u(t-a)f(t-a), where u(t-a) is the unit step function.

In this case, a = 5 and F(s) = -3.

The inverse Laplace transform of F(s) = -3 is simply -3δ(t), where δ(t) is the Dirac delta function.

Therefore, the inverse Laplace transform of F(s) = -3e^(-5s) is -3u(t-5)δ(t-5).

This means that the function is 0 for t < 5 and -3 for t = 5.

Knowee AI · Accepted Answer

The inverse Laplace transform is used to revert a function from the frequency domain (s) back to the time domain (t).

Given the function F(s) = -3e^(-5s), we can see that it is a shifted function.

The inverse Laplace transform of a shifted function is given by L^(-1){e^(-as)F(s)} = u(t-a)f(t-a), where u(t-a) is the unit step function.

In this case, a = 5 and F(s) = -3.

The inverse Laplace transform of F(s) = -3 is simply -3δ(t), where δ(t) is the Dirac delta function.

Therefore, the inverse Laplace transform of F(s) = -3e^(-5s) is -3u(t-5)δ(t-5).

This means that the function is 0 for t < 5 and -3 for t = 5.

Determine the inverse Laplace Transform of the functionF(s)=−3e−5s