Laplace Transform of Periodic Function
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The document discusses the Laplace transform of periodic functions, defining a periodic function and presenting a theorem regarding the transformation of piecewise continuous periodic functions. It includes mathematical expressions and integrals related to the Laplace transform and periodic functions. The document serves as a technical overview intended for students studying advanced engineering mathematics.
Laplace Transform of Periodic Function
- 1. Laplace Transform of Periodic Function By Dhaval Shukla 141080119050 Mechanical Department 3rd Semester Group No. 10 Advanced Engineering Mathematics (2130002)
- 2. Laplace Transform of Periodic Function Definition: A function f(t) is said to be periodic function with period p(> 0) if f(t+p)=f(t) for all t>0. Theorem 1: Transform of Periodic Functions − The Laplace transform of a piecewise continuous periodic function f(t) with period p is 0sdtf(t)e 1 1 L{f(t)} 0 st p ps e
- 3. Laplace Transform of Periodic Function We have p dtf(t)edtf(t)e dtf(t)eL{f(t)} st p 0 st 0 st
- 4. Laplace Transform of Periodic Function Put t=u+p in the second integral, 0 susp 0 st 0 p)s(u p 0 st duf(u)eedtf(t)e f(u)u)f(psincedup)f(uedtf(t)eL{f(t)} .u,when tand0up,when tdu,dt
- 5. Laplace Transform of Periodic Function 0 st ps sp 0 st 0sdt,f(t)e e1 1 (s)fL{f(t)} follows.resultdesiredthe(s)fforSolving sfedtf(t)e(s)f
- 6. Laplace Transform of Periodic Function Here is a video defining Laplace Transform of a Periodic Function
- 7. Laplace Transform of Periodic Function 2 0 2 pHere: 2 2 0, t0sinwt, f(t) Re: n Sol t ctifierwaveHalfofTransformLaplaceFindEx
- 8. Laplace Transform of Periodic Function 0 2 2 2 0 2 0 tftf 1 1 tf 1 1 tf 1 1 tfL functionperiodicof.T.LofdefinitionBy dtedte e dte e dte e stst s st s p st ps
- 9. Laplace Transform of Periodic Function s s st st s st s st s e s e s s e s s e e tts ws e e dtte e 222 22 222 0 222 0 2 1 1 1 0cos0sin cossin 1 1 cossin 1 1 sin 1 1