1. Find the Laplace transform of the piecewise defined functions f(t) (illustrated below) by expressing the functions in terms of the piecewise function and the Heaviside step function, H(t). (a) Find L[f(t)]. Assume that 0 < a

Q: Find the Laplace transform of each function: y = S(x)

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Q: Get the function in algebraic form, state its representation in terms of the function unit step and…

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

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Q: Consider the function 1. Write the function in terms of unit step functions. f(t) = (Notation: write…

A: Here we have to write the given piecewise function in unit step function and find the laplace…

Q: a) Find the Fourier transform of 4 f(t) = e tu(t) + -tu(t) + ²9.

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Q: 6. Find the inverse Laplace transform of the function (3²-²)(as + b) I(s) = (s² + a²) (s² + 3²)

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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: 2. Determine the inverse Laplace transform of F(s) F(s) = (25-18)/(s²+9))

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

Q: What would be the laplace transform of a function of f or L{f(t)}?

A: Given: What would be the Laplace transform of a function of f or L{f(t)}?

Q: f(t) A 10 0 2 4 6 t

A: We have to solve given problem:

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: 5. Find the inverse Laplace transform of the function as + b H(s) : (8 – a)2 + B2"

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Q: 6. Find the inverse Laplace transform of the function (B² – a²)(as + b) (s² + a²)(s² + B²)" I(s) =

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Q: 2-find the laplac transform for the function: t² (u-1)

A: Introduction: Laplace transform is named in honour of the great French mathematician, Pierre Simon…

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…

Q: Q1) a) Find L[ (k - ht)².t²] RI Find the Laplace transform of: f (t)= et, cos² (3t)

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Q: 3. Find the inverse Laplace transform of the function (a - B)2 2(a - B)3 (s - a)(s – B)3 a - B F(s)…

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Q: Set if 0<t< 2 Given the function f(t) = if 2<t. Express f(t) in terms of the shifted unit step…

A: Since ft=0 for 2≤t and t&lt;0 so create step function: ut-ut-2 which will give those zero values.…

Q: B/ Find the Laplace transform of f(t) defined as: f(t) = (t-1, (3-t, when 1< t <2 when 2 < t <3

A: Let's find laplace transform of given function.