1. a) The piecewise continious function f(t) in the Figure is considered sum functions, f(t)=f₁(t)+f2(t)+... fn(t). Find f₁(t), f2(t),.., fn(t). b) Find the Laplace Transform of the f(t) function. +f(t) 2 2 4 t

Q: Find the inverse Laplace transform of the function as + b H(s) = (s – a)2 + 32 °

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Q: Find the Laplace transform F(s) = L {f(t)} of the function f(t) = (3 – t) (u₂(t) — u₁(t)) F(s) = L…

A: Formula of Laplace transform  Lu(t-c)=e-cssLtkf(t)=(-1)kdkdsk(F(s))

Q: L Find the Laplace transform F(s) = {f(t)} of the function f(t) = et-2h(t-2), defined on the…

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Q: 2 F(s) 4 e-2s + s2 3 e-s s2 a) Find the inverse transform of F (s) b) Sketch the graph of f(t) c)…

A: (a) Given that Fs=2s-3 e-ss2+4 e-2ss2 Applying inverse Laplace transform on both sides L-1Fs=L-12s-3…

Q: consider the function +61 f(t) = 7, 15+44 | (+-4), +24 1) write the function in terms of unit step…

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Q: For f(t) = e-t – 1, find the Laplace transform of t Then, for g(t) = e-t – 2, (9(t) examine if the…

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Q: Find Laplace transform of the function f(t) = cos(2t + 3)+e¬'u(t – 4) + tcosh²2t

A: Use the following formulas while calculating the Laplace transform of the given function.…

Q: Find Laplace transform of the function f(t) cos(4t + 5) + e-tu(t – 6) + tcosh²4t

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the Laplace transform F(s) = L {ƒ(t)} of the function f(t) = (9 – t) (u₂(t) — u6(t))

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Q: 6. a) Find the Fouriér Transform of f(x) = 1-x² (x) 1), b) Evaluate, - I Cosx-sinx cosdx

A: We have to solve the given problem using Fourier transform.

Q: Given 30<t ₹2 10 elsewhere find Fw), the Fourier transform of ƒ(t). Compute the values of F(0), F(1)…

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Q: Find the inverse Laplace transform L-{F(s)} of the function e-2s F(s) : %D s2 + 5s – 50 NOTE:…

A: Given that Fs=e-2ss2+5s-50 We have to find the inverse Laplace transform of Fs that is L-1Fs For…

Q: Find the inverse Laplac Transform of the following functions: 1 (i) s2+2s+1 s3 -s2+s–1 (iii) TD-2)…

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Q: (a) Find the Laplace transform of the functions: f(t) = tsint+e-4+74³ +44.

A: Sol:- Ltsint+e-4t+7t3+44Use the linearity property of Laplace Transform:For functions ft, gt and…

Q: How is the existence of the Laplace transform of a function guaranteed?

A: We known that the  Existence of the Laplace transform of a function guaranteed

Q: Find the inverse Laplace transform L-{F(s)} of the function F(s) s2 + 9s – 10 NOTE: The answer…

A: The given problem is to find the inverse Laplace transform of the given function.

Q: Let F(s) be the Laplace transform of f(t) = cos (k(t – 7)] e" sin(37)dr, where k is a positive…

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Q: What is the Laplace transform of the function: F (1) = cosh 4t where cosh 4t = A $2– 16 B s2– 16 s2–…

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Q: = Find the inverse Laplace transform f(t) = £¹{F(s)} of the function F(s) = f(t) = = L 6s+2 s² + 100…

A: The function: Fs=6s+2s2+100. We have to find the inverse Laplace transform of the given function.

Q: Obtain the Fourier transform of the function where f(x) = 0 for x &lt; 0 and f(x) = e−axsin(bx) for…

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Q: 8 Find the inverse Laplace transform of F (s) = f (t) = 8"H(t) (Write eab as exp(a*b)). %3| ||

A: We have to find laplace inverse of F(s)

Q: a) Express f(t) in terms of unit step functions b) Find the LaPlace transform of f(t)

A: a) Express the given function in terms of unit step function as follows. ft=2, for all…

Q: Find the inverse Laplace transform f(t) = L¹{F(s)} of the function F(s) = = f(t) = L -- {7+5)-1…

A: Solution:-

Q: A function f(t) has Fourier transform, F(w) we. What are the Fourier transforms of: (a) f(t-3) (b)…

A: If F(ω) is the Fourier transform of f(t), then using the property of shifting, it can be written…

Q: Find the convolution of f(t) = 3t and g(t) = sin (21). You can either calculate f * g directly, or…

A: In the given problem we have to find the convolution of two function f(t) and g(t) using the…