Question

Use the Laplace Transform Table (LTT) to find F(s)=L{f(t)}(s) if f(t)=(sint+cost)²

Answer 1

To find the Laplace transform of f(t)=(sin(t)+cos(t))^2, expand the square and find the individual transforms of each term using the Laplace Transform Table (LTT). Then, sum up the individual transforms to get the final transform F(s).

Step-by-step explanation:

To find the Laplace transform of f(t)=(sin(t)+cos(t))^2 using the Laplace Transform Table (LTT), we can apply the properties of the Laplace transform. First, we expand the square:

f(t) = sin^2(t) + 2sin(t)cos(t) + cos^2(t)

Then, we can use the Laplace transform table to find the individual transforms of each term. The Laplace transform of sin^2(t) is 1/(2s) - 1/(2(s^2+1)), the transform of 2sin(t)cos(t) is 1/s, and the transform of cos^2(t) is also 1/(2s) + 1/(2(s^2+1)).

Finally, we sum up the individual transforms to get the final transform:

F(s) = 1/(2s) - 1/(2(s^2+1)) + 1/s + 1/(2s) + 1/(2(s^2+1))