Discussion in 'Math' started by priya, Aug 19, 2005.
chk out any engineering math textbook or search for it on google ...there are plenty of online tutorial for laplace's transformations and their applications
as far as the textbooks are concerned you can check out advanced engineering mathematics by erwin kreyszig
Perhaps you could be more specific with your query.
For a function f(t) defined for t ≥ 0, the Laplace Transform for that function, (F(s) = L[f(t)]) is given by:
F(S) = L[f(t)] = ∫ e^(-st)*f(t) dt
Integrated from 0 → ∞ , where s is the s-plane variable. The s-plane variable may be a difficult concept to first get your head around, but the relationship between t and s is the same as that between time and frequency. This is a common use of the Laplace and Fourier Transforms
For any function f(t) there is a Laplacian solution (provided the solution exists) that can be calculated using the above equation. For common functions there can be solutions quoted with out proof. A link of some of them can be found here, but there are many more if your care to dig around the internet (Wikepedia has a good article on Laplace Transforms)
If your asking what's the point of Laplace Transforms, well they allow us to look at a dynamic system which is characterised by an n-th order differential equation and by taking Laplace Transfoms (usually by recognising the common solutions shown in the above link) work a solution by simple algebra and multiplication - no need to do any calculus
If you post a more specific query about Laplace Transforms, I'm sure the forum members can help you with it. Failing that I will also recommend the textbook specified by haditya - Advanced Engineering Mathematics by Erwin Kreyzig
hey !is there anyone who can help me.i'm getting confused about the laplace transforms for RC circuit.wether the term denoting the voltage of a charged capacitor has a -ve or +ve sign if it is on the left of the =n.remember the capacitor is being discharged through a resistor.
Can you be clearer with your query?
dave !rose here.got my id expired so logged in as rosie.i was asking about laplace for RC circuit.consider a charged capacitor is being discharged through a resister and the voltage across capacitor being Vc with a source voltage of Vo. can i write it as follows.
Vr +Vc =Vo
where Vr the drop across resistor.
or should i write as
Vr - Vc = Vo
definitely the source and the capacitor voltage will have opposite polarities.
I(s)*R +I(s)[1/cs - 1/c* di/dt(0+) ] = V/s
is it write.
Well I am going to assume you are talking about the following RC circuit arrangement from your question: see here. If my assumptions are wrong please upload a circuit diagram and I will help you with that diagram.
The only difference you need to make from the link is that Vin = Vo.
Therefore, Vo = Vr + Vc
Vr = iR
i = C(dVc/dt)
From the above equation:
Vo = iR + Vc
Substituting for i:
Vo = RC(dVc/dt) + Vc
Using Laplace Transforms and rearranging:
sRC*Vc(s) + Vc(s) = Vo(s)
Vc(s)[sRC + 1] = Vo(s)
You could also apply Kirchoff's Voltage Law to extrapolate the circuit representation in terms of currents:
Vo(s) = R*I(s) + (1/sC)*I(s)
Hope this gives you a few pointers as to your query. If this is not what you are looking for please upload a diagram of the RC circuit arrangement and I'll try and give you a few pointers on it.
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