Question

I need help with a differential equation problem please!!!

Answer 1

Determine the laplace transform of f when f(t)=t, 0<t<2, and f(t) has period 2

Answer 2

\[L[{\prod}{_a,_b}(t)](s)=\frac{ e ^{-as}-e^{-bs} }{ s }\]
This is a property I was given and I believe this should somehow apply here. The problem is that I don't understand what the property is, or how to use it. When I plug in numbers where I think it is appropriate I don't come anywhere close to the answer. Please help me understand the idea here.

Answer 3

Chris: Have you considered what the graph of this (periodic) function looks like? It'd start immediately to the right of t=0, increase to almost 2 as t increases to almost 2, drop to zero, and then repeat.

Answer 4

Yes

Answer 5

Were we to concentrate solely on the first "cycle", we'd be looking at the function f(t)=t only on 0<t<2. In other words, f(t)=t would turn ON at t=0+ and OFF just before t=2.

Mathematically, this function would be written as