Question

Write a formula for f(t) as a sum of Heaviside functions. Type uc for the Heaviside function that jumps at c (don't type uc(t)).

{ t, 0 ≤ t ≤ 2
f(t) = { 2t-2. 2 < t ≤ 4
{ 6, 4 < t
f(t) = ____
Now compute the Laplace transform F(s) = _____

Answer 1

To write f(t) as a sum of Heaviside functions and compute the Laplace transform F(s), we can express the given conditions using Heaviside functions uc(t) and use the formulas for the Laplace transform of Heaviside functions.

Step-by-step explanation:

To write the formula for f(t) as a sum of Heaviside functions, we need to express the given conditions using Heaviside functions uc(t). The function f(t) is defined as follows: f(t) = uc(t) * t + uc(t-2) * (2t - 2) + uc(t-4) * 6

To compute the Laplace transform F(s), we use the properties of the Laplace transform and the formulas for the Laplace transform of Heaviside functions. The Laplace transform of each term in the formula for f(t) can be calculated separately. The resulting Laplace transform is: F(s) = 1/s^2 + (2e^-2s)/s^2 + (6e^-4s)/s