Solve The fallowing funcbions by using Laplace transformahions

Q: Find the laplace transform of x(t)=tcosh(6t) Select the correct response: (s^2 + 36) /[(s^2 -36 )^2]…

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Q: Use the Laplace transform to solve the initial value problem y'" + y' – 2y = 2e*, y(0) - - 1, y'(0)…

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Q: Laplace transform for e -t u( t) + e -2t u( t) is

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Q: Use the first translation principle and the basic Laplace formulas to find the inverse transform of…

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Q: Find the Laplace transform (3)

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Q: 3. State and explain the Convolution Theorem for Laplace transform

A: To prove: State and explain the convolution theorem for Laplace transform.

Q: Find the Laplace transform of sint 0<t<27 f() =

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Q: бу"" + 5у" + у'%3D0 У (0) %3D — 2, у' (0)%3 2, у" (0) 3D 0

A: We have 6y'''+5y''+y'=0 with initial conditions y0=-2, y'0=2, y''0=0 Now, apply Laplace transform on…

Q: 4 f4* u lt - i) + (+1) u(t -)

A: Some of the properties of the Laplace transform   Lu(t-c)=e-cssLf(t)+g(t)=F(s)+G(s)L[af(t)]=aF(s)

Q: WHAT IS THE LAPLACE TRANSFORM OF THIS? -3(1-cosh 377t) t.

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Q: What is the Laplace Transform of e^t?.

A: To find the Laplace Transform of et  L(et)   By definition, L(f(t)) = ∫0∞ e-st  f(t)  dt

Q: 3 2t Find the laplace transform of ett²+ e²t (2cos 3t). - 16

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Q: Please find the Laplace transform of et for t > s

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Q: Q3\Find the Laplace transform of: a) t et * sin(4 t)

A: Given  f(t)= tet sin4t

Q: 1 If the Laplace transform of ewt is , the Laplace transform of t coshtis S-W

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Q: find the Laplace transform of t²cos(wt)

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Q: Determine the Laplace transform of the equation f (x) = 2e-"sin4t 16 A s2+ 4s + 20 20 B s2+ 4s + 20…

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Q: 2. Verify the following property of the Fourier transform: F(u(x + a)) = e-ial a(z)

A: Given::- Verify the following property of the Fourier transform: F(u(x + a)) =e^ -ia xi hat u( xi).

Q: infinty use L.23 and L32 of Laplace Transform Table to evaluate Ţ [t] (2t). dt. 0

A: The integralThe Laplace transform of the function f(t)Now, from the Bessel function of the First…

Q: 3. Find 4 {0 21 jucosudu } using the properties of Laplace transform.

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Q: 5) Use Laplace transform to solve the integrol epuation it f(t) = cost + (*- tau) e

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Q: f(t) = cos 5t – 3t² s4-6s2-30 s4-6s2-150 а. F(s) с. F(s) s5+25s3 5s3-6s²–150 s5+5s3 5s3-6s2-30 b.…

A: We need to find the Laplace transform of ft=cos 5t-3t2 That is we need to find Lcos 5t-3t2 Now,…

Q: Q1. a) Derive the Laplace transform of 3e4t from first principles (i.e. without using the list of…

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Q: Determine the Laplace transform o sin (8t + 붕). +64 -a +(a) #() +64 +64 O 43 #() 2+64 O 4v3 7+64…

A: We need to find Laplace transform of sin8t+116π Here we will us the following formulas-…

Q: Q4.) F(s) L' = 45+93 252+85+40 } 45+9 252 = = 2 = +85+40 =2 2 L" { -1 L+ تو 2/2-1 -2t ? (pat し S+…

A: Here we use the sum and product by scale of Laplace transformation.

Q: Find the Laplace transform using convolution theorem: Te2" sin(2(t - T))dr.

A: So, here f(t) = sin(2t) and g(t) = t e2t.

Q: Use Laplace transform to solve IVP shown below: у" — 5у' + бу %3D2tet - Зet | У (0) %3D 1, у'(0) %3…

A: Given y''-5y'+6y=2 t et-3et, y(0)=1,  y'(0)=-1   To Use Laplace Transform to solve the given IVP

Q: -et Cos wot Z a tj w 2 t Wo

A: We have to use Fourier transform formula.

Q: What is the Laplace transform of x (t) = e^- t cosπt ? Select one:

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Q: ce transform to sa yu + 3y! +2g S

A: Given differential equation is, y''+3y'+2y=6e-t       ........1 It is known if, Lft=Fs then,…

Q: 2) fece). (1-+*)* + + cos

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Q: Find the Fourier Cosine Transform of the function ƒ(x) = (ae-4x + be-³x + ce-²x)² if x > 0 if a = 4,…

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Q: xt) t osh 3t sinh 3t + ws (ot - )

A: If f(t) is a function of t defined for all positive values of t. Then, the Laplace transform of the…

Q: у"" + Зу" + Зу' %3D у У(0) 3D 7, у' (0) — -7, у" (0) — 11

A: We have to apply the Laplace transform method.

Q: -4s Using Laplace transform tables or otherwise, find L-1

A: Please check step 2 for the solution.!

Q: oくくく 1.

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Q: Inverse Laplace transfor a. etsin4t b. 1/2etsin4t

A: This is a problem of Laplace transform.