Heaviside function

[Uniman]

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
Report Abuse
Is the answer correct.....​

 

[CaptainBlack]

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
Is the answer correct.....​

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 \(x=5\) )

Also remove the link from your post.

CB