I agree with your answers for A and C, but I get something different for B.engnrshyckh said:Summary:: I want to find inverse laplace of function 1/s(s^2+w^2)
I used partial fraction method first as:
1/s(s^2+w^2)=A/s+Bs+C/(s^2+w^2)
I found A=1/w^2
B=-1
C=0
engnrshyckh said:1/s(s^2+w^2)=1/sw^2- s/s^2 +w^2
Taking invers laplace i get
1/w2 - coswt
But the ans is not correct kindly help.
Tell me?Mark44 said:I agree with your answers for A and C, but I get something different for B.
Comparing the Coefficient of s^2 i get (1+B)/w^2 =0 which give me B=-1engnrshyckh said:Tell me?
Multiply both sides by ##s(s^2 + w^2)##. What do you get in the next step?engnrshyckh said:Summary:: I want to find inverse laplace of function 1/s(s^2+w^2)
1/s(s^2+w^2)=A/s+Bs+C/(s^2+w^2)
1=A(s^2+w^2)+BS^2+CsMark44 said:Multiply both sides by ##s(s^2 + w^2)##. What do you get in the next step?
For finding Bengnrshyckh said:1=A(s^2+w^2)+BS^2+Cs
Right, so A + B = 0, and also Aw^2 = 1, so what do you now get for B?engnrshyckh said:For finding B
As^2+Bs^2=0
Thanks - 1/w2Mark44 said:Right, so A + B = 0, and also Aw^2 = 1, so what do you now get for B?
engnrshyckh said:Thanks - 1/w2
An inverse Laplace transform is a mathematical operation that takes a function in the complex frequency domain and transforms it back into the time domain. It is the reverse of the Laplace transform and is used to solve differential equations and analyze systems in engineering and physics.
The inverse Laplace transform is calculated using a table of known transforms or through the use of integration techniques. It involves finding the original function from its Laplace transform by taking the integral of the transform with respect to the complex variable s.
The inverse Laplace transform has several properties, including linearity, time shifting, and frequency shifting. It also has a convolution property that allows for the transformation of complex functions into simpler ones. Additionally, it has a uniqueness property, meaning that a function cannot have more than one inverse Laplace transform.
Inverse Laplace transform has various applications in engineering, physics, and mathematics. It is used to solve differential equations and analyze systems in control theory, signal processing, and circuit analysis. It is also used in the study of heat transfer, fluid dynamics, and quantum mechanics.
The inverse Laplace transform can only be applied to functions that have a Laplace transform. It also requires advanced mathematical skills and can be time-consuming to calculate. Additionally, it may not always give a closed-form solution, and numerical methods may be required to obtain an approximate answer.