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) = ___

Answer 1

To write the function f(t) as a sum of Heaviside functions, we need to express f(t) in terms of intervals where different functions apply. Then, we can write f(t) as a sum of Heaviside functions using the given intervals.

Step-by-step explanation:

To write the function f(t) as a sum of Heaviside functions, we need to express f(t) in terms of intervals where different functions apply. First, let's break down the given function into three intervals:

1. For 0 ≤ t ≤ 2: f(t) = t
2. For 2 < t ≤ 4: f(t) = 2t - 2
3. For t > 4: f(t) = 6

Now, we can write f(t) as a sum of Heaviside functions:

f(t) = t * uc(t - 0) + (2t - 2) * uc(t - 2) + 6 * uc(t - 4)