Graph the piecewise function and get its laplace transform. 0 h(t) = sin / 3t t 0 T 2 t <0 0 < t < ²2/1/20 3 25 Lt 16 t 26

Q: Q1: Find Laplace transform for the following functions 1) f(t)=t cos(@t)

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Q: f(t) = v1+ sin t + (6t)13 + t² sin 4t

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Q: Find the Laplace transform of: 1. f(t) = e(-3t) sin(2t) cos(3t) cosh(t)

A: Given that 1) f(t) = e-3tsin (2t) cos (3t) cosh (t) 2) f(t) = 1+sin t + (8t)15 + t2cos 3t We have to…

Q: Derive the Laplace transform for the following time functions: a. u(t) tu(t) b. C. sin wt u(t) d.…

A: As per Bartleby rules we have to answer only first three questions.

Q: tet-t Find the inverse Laplace transform L{F(s)} of the function -8s F(s) = s2 + 6s – 16 | NOTE:…

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Q: 3. Write each function in terms of unit step functions. Then, find the Laplace transform. -2 0π

A: a.) Unit Step Function: f(t) = -2u(t) + 2u(t - 3) + (t-4)u(t-3)     Laplace Transform:…

Q: 2as L{t sin(at)} = %3D (s²+a²)²

A: We can derive it using the definition of Laplace transform or by using some identify or formula.

Q: 8. Express the given function using unit step functions and compute its Laplace transform y sin t N…

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Q: 1.1) Calculate the Laplace transform of the following function from first principles: √3t -1 0<t<1 0…

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Q: 2 - ƒ (t) = sin 0.5t + ²⁄t – 3 8 cos 32t

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Q: Q.12 Use the Laplac transform to solve the I.V.P: ty'-y = 0, y(1) = 3.

A: We have to find the particular solution of the given initial value problem using the Laplace…

Q: 7. L {f(t)} where f(t) = t sin 2t sin 5t %3D

A: Use the trigonometric identity sin Asin B=12cosA-B-cosA+B to simplify the given function.

Q: n of each function. N

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Q: sin 3t 4. f (t) t

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Q: Sketch the given function, which is assumed to be zero outside the given interval. Find its Laplace…

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Q: Find the laplace transform of cos at using the formula £{ƒ (t)} = est f (t) dt. Hencefind the…

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Q: a. f(t)= et, cost, 0 2TT.

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Q: 3. f(t) = cosh(3t) %3D

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Q: 1. Write the following function using unit step functions and then find its Laplace transform: 2t 0…

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Q: Express the given function in terms of unit step functions, and find its Laplace transform. sin t, 0…

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Q: 2. f (t) = sin ( € - 2π) H ( t - 21)

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Q: 1. Find the laplace transform of the following equation i. f(t) = t sin 3t ii. f(t) = t iii. f(t) =…

A: Solution

Q: Find the Laplace Transform of f(t) = {°. 0 st 3

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Q: SOLVE FOR THE LAPLACE TRANSFORM OF THE GIVEN EQUATION. Jell 2. f(t) = cosh wt sin wt

A: The function cosh(ωt) can be rewritten as eωt+e-ωt2. Thus, ft=cosh(ωt)sin(ωt) can be rewritten as…

Q: Use the method of laplace transform to solve f(t). t ƒ ( t) = 2t 4/s xf (tx) dx 2t - 4 sin

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Q: Consider the function if 0 <t < 6T f(t) sin(t – 67) if 67 < t. a. Use the graph of this function to…

A: At first we would convert the function into heaviside function and then use it to find laplace…

Q: . Determine the Fourier transform of the following: (t) = {e ¹³6, -1 < t < 1 elsewhere

A: We know formula for Fourier transform of f(t) F(ω)=∫-∞∞f(t).ejωtdt we have…