If L\left\{f(t)\right\}=F(s) , then L{f(4t)} (a)frac(1)(4) F(s) (b)F(frac(s)(4)) (c)4F(s) (d)frac(1)(4) F(frac(s)(4))

Ernstfalld 2021-09-23 Answered

If Lf(t)=F(s),  then  Lf(4t)
a) 14F(s)
b) F(s4)
c) 4F(s)
d) 14F(s4)

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Expert Answer

opsadnojD
Answered 2021-09-24 Author has 95 answers
Step 1
Here we solve this from the definition of Laplace transformation.
step 2
L(f(t))=F(s)=0f(t)estdt
L(f(4t))=0f(4t)estdt
Step 3
Let us take transformation z=4tdt=dz4
Then the integration becomes
L(f(4t))=0f(4t)estdt=0f(z)esz4dz4
=140f(z)es4zdz=14F(s4)
Step 4
The final answer is L(f(4t))=14F(s4) so 4th option is correct.
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