Heaviside function

Uniman

New member
Consider the function

Then f(t) can be expressed with Heaviside functions as

Determine b.

Workdone so far......

f(t) = 7H(t) + bH(t-5)
when t = 5
f(5) = 49 + 7b
15 = 49 + 7b
-34 = 7b
b = -34/7
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CaptainBlack

Well-known member
Consider the function

Then f(t) can be expressed with Heaviside functions as

Determine b.

Workdone so far......

f(t) = 7H(t) + bH(t-5)
when t = 5
f(5) = 49 + 7b
15 = 49 + 7b
-34 = 7b
b = -34/7
As it is written your function cannot be written as a combination of Heaviside steps, since such a combination is defined on the whole real line, but the domain of your function is just the positive real line. So you either to use Heaviside steps restricted to the $$x>0$$ of you need to specify that your function is zero foir $$x<0$$.
Anyway what you probably want is $$f(x)=7H(x)+8H(x-5)$$ and then to check that this is correct at the steps (this is $$0$$ up to $$0$$, $$7$$ from $$0$$ to $$5$$ and $$7+8=15$$ past $$x=5$$ )