Find the Laplace Transform of g(t)={(5sin(3[t-frac{pi}{4}]) , t>frac(pi)(4)),(0 , t<frac(pi)(4)):}

CMIIh

CMIIh

Answered question

2021-09-10

Find the Laplace Transform of g(t)={5sin(3[tπ4])t>π40t<π4

Answer & Explanation

yunitsiL

yunitsiL

Skilled2021-09-11Added 108 answers

Step 1
Consider the provided question,
g(t)={5sin(3[tπ4])t>π40t<π4
It can be written as,
g(t)=0+u(tπ4)(sin(3[tπ4])0)
=u(tπ4)(sin(3[tπ4]))
=u(tπ4)[sin(3t)cos(3π4)cos(3t)sin(3π4)]
=12u(tπ4)[sin(3t)cos(3t)]
Step 2
Use Laplace Transform L{g(t)}
=12L{u(tπ4)(sin3t+cos3t)}
=12eπ4sL{sin3t+cos3t}
=12eπ4s{s+3s2+9}
L{g(t)}=12eπ4s{s+3s2+9}

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