Inverse Laplace Transform of S/(S2+1) (S2+4)^2
Answers
Answer:
s • (s2 + 4)2
—————————————
s2 + 1
Step-by-step explanation:
s
Simplify ——————
s2 + 1
Polynomial Roots Calculator :
1.1 Find roots (zeroes) of : F(s) = s2 + 1
Polynomial Roots Calculator is a set of methods aimed at finding values of s for which F(s)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers s which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is 1.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 2.00
1 1 1.00 2.00
Polynomial Roots Calculator found no rational roots
Equation at the end of step
1
:
s
—————— • (s2 + 4)2
s2 + 1
STEP
2
:
Polynomial Roots Calculator :
2.1 Find roots (zeroes) of : F(s) = (s2+4)2
See theory in step 1.1
In this case, the Leading Coefficient is 1 and the Trailing Constant is 4.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,4
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 5.00
-2 1 -2.00 8.00
-4 1 -4.00 20.00
1 1 1.00 5.00
2 1 2.00 8.00
4 1 4.00 20.00
Polynomial Roots Calculator found no rational roots
Final result :
s • (s2 + 4)2
—————————————
s2 + 1