Question

Using a hand calculation, find the Laplace transform of

f(t) = 0.0075 - 0.00034e⁻².⁵ᵗ cos(22t) +0.087e⁻².⁵ᵗ sin(22t) - 0.0072e⁻⁸ᵗ

Answer 1

The Laplace transform of the given function f(t) is explained step by step.

Step-by-step explanation:

To find the Laplace transform of the function f(t) = 0.0075 - 0.00034e-2.5tcos(22t) + 0.087e-2.5tsin(22t) - 0.0072e-8t,

we can use the linearity property of Laplace transforms. The Laplace transform of each term can be found using the standard transform pairs.

Using the transform pairs, we get:

L{0.0075} = 0.0075/s

L{-0.00034e-2.5tcos(22t)} = -0.00034/(s+2.5)/(s+2.5^2+22^2)

L{0.087e-2.5tsin(22t)} = 0.087/(s+2.5)/(s+2.5^2+22^2)

L{-0.0072e-8t} = -0.0072/(s+8)

Adding up these transformations gives:

L{f(t)} = 0.0075/s - 0.00034/(s+2.5)/(s^2+5s+572) + 0.087/(s+2.5)/(s^2+5s+572) - 0.0072/(s+8)