Find Laplace transform of the given function te−4tsin⁡3t

Tobias Ali

Tobias Ali

Answered

2020-11-06

Find Laplace transform of the given function
te4tsin3t

Answer & Explanation

opsadnojD

opsadnojD

Expert

2020-11-07Added 95 answers

Step 1
Concept Used:
L{tkf(t)}=(1)k(dk)L{f(t)}dsk
also,
L{sin(at)}=a(s2+a2)
L{ebtsin(at)}=a(s+b)2+a2
Step 2
Given: Given function is f(t)=te4tsin(3t)
We want to calculate Laplace transform
Calculation:
Given function is f(t)=te4tsin(3t)
Therefore,
L{f(t)}=L{te4tsin(3t)}
=(1)1d[L{e4tsin(3t)}]ds
=dds[3(s+4)2+9]
=dds[3s2+8s+16+9]
=dds[3s2+8s+25]
=3d(s2+8s+25)1ds
=3(1)(s2+8s+25)2d(s2+8s+25)ds
{By chain rule }
=3(s2+8s+25)2(2s+8)
L{f(t)}=6(s+4)(s2+8s+25)2
Step 3
Answer: The Laplace transform of f(t)=te4tsin(3t) is L{f(t)}=6(s+4)(s2+8s+25)2

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