Heaviside / Convoltuion Graph

Apr 2009
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Hi all, i need some hints in how to start this problem...

Suppose \(\displaystyle f(t) = tH(t)\) and \(\displaystyle g(t) = t^2H(t)\)

a) Sketch the graph of \(\displaystyle f(t)\) and \(\displaystyle g(t)\) over the interval \(\displaystyle 0 \leq t \leq 2\)

I can see part of the graph on Wolfram but I'm pretty stuck...
 

CaptainBlack

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Hi all, i need some hints in how to start this problem...

Suppose \(\displaystyle f(t) = tH(t)\) and \(\displaystyle g(t) = t^2H(t)\)

a) Sketch the graph of \(\displaystyle f(t)\) and \(\displaystyle g(t)\) over the interval \(\displaystyle 0 \leq t \leq 2\)

I can see part of the graph on Wolfram but I'm pretty stuck...
The graphs of \(\displaystyle f(t)\) and \(\displaystyle g(t)\) are identical to those of \(\displaystyle t\) and \(\displaystyle t^2\) on \(\displaystyle 0<t \le 2\) as \(\displaystyle H(t)=1\) on this interval. Also as \(\displaystyle f(0)=g(0)=0\) the plots may be extended to the closed interval in the obvious way.

CB
 
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