Compute the Inverse Laplace Transform of F(s) =frac{s}{R^2s^2+16pi^2}take R=70

CoormaBak9 2021-01-31 Answered

Compute the Inverse Laplace Transform of F(s)=sR2s2+16π2
take R=70

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Expert Answer

Khribechy
Answered 2021-02-01 Author has 100 answers

Step 1
Given that, R=70.
The given function is, F(s)=sR2s2+16π2
F(s)=s702s2+16π2
F(s)=s4900s2+16π2
f(t)=L1(s4900s2+16π2)
It is known that, L1(sF(s))=d(dt)f(t)+f(0)
Step 2
Apply the above property and obtain the inverse Laplace transform of the given function as shown below.
f(t)=L1(s4900s2+16π2)
f(t)=L1(14900s2+16π2)+L1(14900s2+16π2)(0)
f(t)=d(dt)(1280sin((2πt)35))+0
f(t)=14900cos(2πt35)
Thus, the required inverse Laplace transform is obtained.

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