Derive the Laplace transform of the following function sin(h(at))

Harlen Pritchard 2021-02-05 Answered
Derive the Laplace transform of the following function
sin(h(at))
You can still ask an expert for help

Want to know more about Laplace transform?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

okomgcae
Answered 2021-02-06 Author has 93 answers
Step 1 We have to derive the Laplace transform of function:
sin(h(at))
We know from definition of hyperbolic function,
sinhx=exex2
If x=at then,
sinhx=exex2
sinhat=eateat2
=12(eateat)
Step 2
Now finding Laplace transform,
L(sinhat)=L(12(eateat)
=12(LeatL(eat))
We know the Laplace transform of exponential function,
L(eax)=1(sa)
if a=-a then L(eax)=1(s+a)
Putting Laplace transform of exponential function, we get
12(LeatL(eat))=12((1(sa))(1(s+a))
=12(s+a(sa))(sa)(s+a)
=12(s+as+a)(s2a2) since (since(a+b)(ab)=a2b2)
=122a(s2a2)
=as2a2
Hence, Laplace transform of sinhat is a(s2a2)
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more