annamation
Nov3-09, 01:22 AM
1. The problem statement, all variables and given/known data
Find the Laplace transform of f(t) where
f(t)={ 3 if 0<=t<2
2t^2+2 if 2<=t<3
-4 if t>=3
2. Relevant equations
3. The attempt at a solution
We where taught to approach this from a "turn-off, turn-on" strategy where
f(t)=3-3(u2)+(2t^2+t)u2-(2t^2+t)u3-4u3
you then group together the u2 and u3 terms to get
3+(2t^2+t-3)u2- (2t^2+t+4)u3
in the past from this step you try and get what's being multiplied by u2 and u3 in terms of (t-3) and (t-2) respectively. and then take the Laplace transform of it as though the (t-3) and (t-2) term was just t. where u2 becomes e^2t and u3 becomes e^3t. but with 2t^2 I don't know what to do. Can you help please!
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
Find the Laplace transform of f(t) where
f(t)={ 3 if 0<=t<2
2t^2+2 if 2<=t<3
-4 if t>=3
2. Relevant equations
3. The attempt at a solution
We where taught to approach this from a "turn-off, turn-on" strategy where
f(t)=3-3(u2)+(2t^2+t)u2-(2t^2+t)u3-4u3
you then group together the u2 and u3 terms to get
3+(2t^2+t-3)u2- (2t^2+t+4)u3
in the past from this step you try and get what's being multiplied by u2 and u3 in terms of (t-3) and (t-2) respectively. and then take the Laplace transform of it as though the (t-3) and (t-2) term was just t. where u2 becomes e^2t and u3 becomes e^3t. but with 2t^2 I don't know what to do. Can you help please!
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution