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s to find {f(t)} given that-1, 0

Question

Use the definition of Laplace Transforms to find l{f(t)}

See image.

Then rewrite f(t) as a sum of step functions, uc(t), and show that by taking Laplace transforms, this yields the same answer as your direct computation.

s to find {f(t)} given that
-1, 0<t<1
f(t) =
t21
by ta
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s to find {f(t)} given that -1, 0<t<1 f(t) = t21 by ta

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check_circleAnswer
Step 1

Consider the given function:

-1, 0st<1)
f (t
1,
t21
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-1, 0st<1) f (t 1, t21

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Step 2

Now, by definition of Laplace Transform:

L{f(testf()dt
0
1
=je-st f()dt+est f(t)dt
0
1
1
=je st (-1)dt+e-St (1)dt
0
1
e-st
-st0
-S
하045
0+eS
1
Lf(t)=2e
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L{f(testf()dt 0 1 =je-st f()dt+est f(t)dt 0 1 1 =je st (-1)dt+e-St (1)dt 0 1 e-st -st0 -S 하045 0+eS 1 Lf(t)=2e

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Step 3

Now, Rewrite f(t) as the sum of step functions, ...

-1 0st<1
f(t)
1
t1
(-1)01(0+1)(4
-(-)(4 )-40)((4(0)
=-0()+214()
help_outline

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-1 0st<1 f(t) 1 t1 (-1)01(0+1)(4 -(-)(4 )-40)((4(0) =-0()+214()

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