Determine the Laplace transforms of these functions: a)\ f(t)=(t-4)u(t-2) b)\ g(t)=2e^{-4t}u(t-1)

atodion23

atodion23

Answered question

2021-11-17

Determine the Laplace transforms of these functions:
a) f(t)=(t4)u(t2)
b) g(t)=2e4tu(t1)

Answer & Explanation

Squairron

Squairron

Beginner2021-11-18Added 7 answers

a) We can express f(t) as
f(t)=(t22)u(t2)
=(t2)u(t2)2u(t2)
By the linearly and times shift properties,
F(x)=L[(t2)u(t2)]2L[u(t2)]
=1s2e2s2se2s
=(1s22s)e2s
b) We can express g(t) as
g(t)=2e4(t1+1)u(t1)
=2e4e4(t1)u(t1)
By the time shift property,
G(s)=2e4L[e4(t1)u(t1)]
=2e4ess+4
=2e(s+4)s+4

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