The Laplace transform of tu(t-2)=e^{-2s}left[frac{s+2s^2}{s^3}right] True or False?

coexpennan 2021-02-03 Answered
The Laplace transform of tu(t2)=e2s[s+2s2s3]
True or False?
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Expert Answer

Faiza Fuller
Answered 2021-02-04 Author has 108 answers
Step 1
The given function is tu(t2)
To find the Laplace transform proceed as follows
L{tu(t2)} . The function u(t2) is unit step function .
Find the Laplace of u(t2)
L{u(t2)}=e2ss
The function u(t2) is multiplied by t, use the formula for the multiplication by t^n use the formula L{f(t)}=L{f(t)}=(f¯)(s) then L{tnf(t)}=(1)ndndsn(f¯)(s)
here n =1
therefore, L{tu(t2)}=(1)ddse2ss
Step 2
Solve L{tu(t2)}=(1)ddse2ss
L{tu(t2)}=(1)sddse2se2sddsss2
=(1)(s(2)e2se2s(1)s2)
=(2se2s+e2ss2)
=e2s(2s+1s2)ss
=e2s(2s2+ss3)
The Laplace transform of the given function is e2s(2s2+ss3)
The answer is TRUE
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