1. Express the given function f (t) in terms of unit step function and use Second Shifting Theorem to find Laplace transform: L [ƒ (t)]=? t, ƒ(t) = { 2 − t, 6, 2. Use the Second Shifting Theorem to find inverse Laplace transform: L-¹ [F (s)]=? F (s) : = TS (1—2s) 0≤t<1 1≤t<2 t> 2 s² +4s+5

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

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Q: Find Laplace transform of the function from definition: f(t)=sin(2t)

A: The objective of this question is to find the Laplace transform of the function f(t) = sin(2t). The…

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 +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: Find the inverse Laplace Transform of F(s) 2s2 + s -3 F(s) = s4 +3s2 + 2

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Q: 3. Find the inverse Laplace transform of F(s) = 180+18,²+354

A: Applying this to each term:  So, the inverse Laplace transform of F(s) is: f(t)=4t6​+43​t4+23​t2…

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: d.-tte-6c 3

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

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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: F(s) = 1 (s + 1)²(s² + 4)

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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: Find the Laplace transform F(s) = L {f(t)} of the function f(t) = 3e-10t + 9t + 5et, defined for t >…

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