Find the Laplace Transformof the following functions 2as 4) f(t) =tsinh(at) Ans. F(s) = (s² – a° }

Q: 5. f(t) = sin (6t).

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Q: 00 1. Find the laplace transform of, f(t) =sin(t +a)cos(t -a) using e-stf(t)dt.

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Q: Find Laplace Transform of the following function by definition only (Show all steps on integrals)…

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Q: Find the Laplace Transform of the following: (2 3. h(t) = }t t 4

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Q: Using the tables write down the transforms of the following functions/ (i) t² – 3t + 4 (ii) 2 cost…

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Q: Q1: Find Laplace transform for the following functions 4) f(t)=t sinh(at)

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Q: i). ƒ (1) = (5– 312) ² i). ƒ (1) =r2sinh (21) Find the Laplace transforms of the following…

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Q: A function f(t) is given as f(t) = e' cos 2t cos t %3! Find the Laplace transform of this function.

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Q: Find the Laplace transform of the following functions: 1. L{5} 2. L{t³} 3. L{e³t} 4. L{sin 4t} 5.…

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Q: Q4: Find the derivative of the function at P. in the direction of A 2) g(x, y) = x - (y² /x)+ J3…

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Q: If F(s) = -3s² s + 1 is the Laplace transform of f(t), find the following, correct to three decimal…

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Q: 3 find The Laplace transform f(t) = sint

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Q: Q4: Find the derivative of the function at Po in the direction of A 3) f(x, y, z) = xy+ yz + xz,…

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Q: 5. Find the Laplace transform of f(t) = sin't t

A: The laplace transform of f(t)=sin2t

Q: Find the Inverse Laplace Transform of the following: 2. Y(s) = /(2s– 3)5

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Q: Find the inverse Laplace transform L-{F(s)} of the given function. 18 F(s) = s2 + 9 Your answer…

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Q: t も c6 10. XCt)> { -8 + -8 t ct-6)? » t >6

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Q: Using convolution property of Laplace Transform, solve for y(t) of the following: 2) y(t) = sin(nt)…

A: The given problem is to solve for y(t) for the given function by using convolution property of…

Q: i). ƒ (t) = ²) ² ii). ƒ (t) =t²sinh (21) (5–31

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Q: Prove that the Laplace Transform of sin(at)+at cos (at) is 2as? (s` +a°)* Please show your Solution…

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Q: 2s – 7 - F(s) = %3D (s – 4)(s + 6)

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Q: Q3 Find Laplace transform of the function f (t)=t cos(@t)

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Q: Q. No.1 a) Use logarithmic differentiation to find dy/dx of the expression: 3 2(2x+1)(x-3)…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: a. Find the Laplace transform F(s) = L{f(1)} of the function f(t) = sin (wt), defined on the…

A: Here we have to find the Laplace transform F(s)=L{f(t)} of the function f(t)=sin2(wt), defined on…

Q: Find the inverse Laplace transform f(t) = £¯¹ {F(s)} of the function F(s) = e −3s (1 – 4s) s² + 16

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Q: Find the convolution (f * g), after integrating find the Laplace transform of (f * g): f(t) = cos2t,…

A: We have to find convolution (f*g) and the Laplace transform of (f*g) wheref(t)= cos2t, g(t)= et .

Q: 5 The inverse Laplace transform of F(s) = 5² - 2s+5 1 f(t) = 5e²¹ sin 2t f(t) = 5e¹ sin 2t 5 f(t) =…

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Q: 3. Find CH(t) when H(t) = (et-3)(e?-) %3D

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Q: Find the Laplace transform of the given function; a and b are real constants. f(t) = e** sinh(bt)…

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Q: Differentiate the function. P'(W) = P(w) = 6w² - 4w+2 √w W

A: To differentiate the following function.

Q: 5. (Ci | Show that L{e"t"} = n! in two ways: (s- a)n+1 (a) Use the translation property for F(s).…

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Q: Write the function in terms of unit step functions and find the Laplace transform f(t) = { 2, -2, 0…

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Q: Find the inverse Laplace transform L{F(s)} of the given function. 8s2 – 24s + 72 F(s) = s(s² + 36)…

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