Compute the Laplace Transform of the given functions: First, rewrite in terms of step functions! To do this at each step you 'add the jump'. That is, if the formula changes from gi(t) to 92(t) at t=c, then you will have a term of the form u(t) (g(t)- gi(t)) in the function. Second, use L[u(t)f(t-c)}=eC{f(t)}. Another way to write this is C{u,(t)f(t)}=eC{f(t+c)}. Thus, you 'pull out' (t) and write e out in front. At the same time you replace t' with t+e' and find the Laplace function of the new expression. 1. f(t) 0,0 ≤ t < 6: ,t≥ 6. - {% 3
Compute the Laplace Transform of the given functions: First, rewrite in terms of step functions! To do this at each step you 'add the jump'. That is, if the formula changes from gi(t) to 92(t) at t=c, then you will have a term of the form u(t) (g(t)- gi(t)) in the function. Second, use L[u(t)f(t-c)}=eC{f(t)}. Another way to write this is C{u,(t)f(t)}=eC{f(t+c)}. Thus, you 'pull out' (t) and write e out in front. At the same time you replace t' with t+e' and find the Laplace function of the new expression. 1. f(t) 0,0 ≤ t < 6: ,t≥ 6. - {% 3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Question 2:
Compute the Laplace Transform of the given functions:
• First, rewrite in terms of step functions!
To do this at each step you 'add the jump'. That is, if the formula changes from gi(t) to g2(t) at t=c,
then you will have a term of the form e(t) (92(t)- gi(t)) in the function.
. Second, use C(u(t)f(t-c)}=eC{f(t)}.
Another way to write this is C{u(t)f(t)}=e**C{f(t+c)}.
Thus, you 'pull out' (t) and write e out in front. At the same time you replace t' with 't+e' and
find the Laplace function of the new expression.
1. f(0) = { 3
2. g(t) =
,0 ≤ t < 6;
,t ≥ 6.
3. h(t)
3 ,0 ≤ t < 5;
10,5≤t≤8
0 ,t28.
- {%
4. j(t) = {4+5(t
5. u(t) = {(t−7)³ t≥7.
6 sin(t-3),t≥ 3.
,0 ≤ t < 3;
4+5(t2)et-2
6. v(t) = { { t ,t21.
,0 ≤t<7;
,0 ≤ t < 1;
7. w(t) = ·{²/²2 t² ,t24.
,0 ≤ t < 2;
,t> 2.
,0 < t < 4;
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