f(t) = (est + 2t + 1)²

Q: 7. e-at sin(bt) 8. e-at cos(bt) where a and b are constants. where a and b are constants. 9. 1- e-at…

A:

Q: 2s-3 L-1 s2-4s+8

A: To solve this question first we simplyfy the given function and then use the inverse Laplace…

Q: Aşsinst – cos8t} =sin4t

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

Q: Find the transform of the given function by use of a table. f(t) = 4 + -4t cos 39 t

A: Concept: Laplace transformation: Differential equations can be solved using the Laplace…

Q: 1. (a) 2t – 3 (b) 5t²+41 – 3

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Q: - 3t +2 (b) 24 2. (a) 15

A: Topic = Laplace transform

Q: co sh?Ł

A: As we know,    cosht = exp(t)+exp(-t)2                  and               Laplace transform of ept =…

Q: y" + 4y' + 3y = U (t – n)e-2(t-r), y(0) = 0, y'(0) = 0. %3D

A: Consider the provided question,

Q: 3t 3. f(t) = e³t (6t + 1)²

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Q: f(t) = [1– u2m(t)](2 sin t – sin 2t) U2n

A: Some of the properties of Laplace transformation Lsinat=as2+a2Luc(t)=e-cssLuc(t)g(t)=e-csL[g(t+c)]

Q: f(t) = [1– uzn(t)](2 sin t – sin 2t

A: Solution

Q: 3. Evaluate L{4e-2tt3 +t sint cos t}

A: L4e-2tt3+t sint cost

Q: -1, 0≤t≤3 f(t)=2t, 3≤t≤4 1, t> 4

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Q: (d) f(t) est sin(4t)

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Q: Solve the initial value problem below using the method of Laplace transforms. y" +6y' + 8y = -…

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Q: Give 5 simple or basic examples of Laplace Transforms with solution.

A: First example: We have a formula Ltn=n!sn+1 So, one example is for n=2: Lt2=2!s2+1=2s3 Hence,…

Q: 2. Prove that L(cashkt)= và

A: Given question is related with the topic Laplace transform. We have to prove the result that   Lcosh…

Q: f(t) = e³t (sin 2t + cos2t)²

A: We have to find the Laplace transform of the given function.

Q: Q4) Q2) t" ( by definition) find Laplace transformation

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Q: 9. 3 cos(wt –@), where w and a are constants.

A: We use first Cos(a-b)=cos(a) cos(b)+sin(a)sin(b) and then we use Laplace transform of…

Q: 3. (а) 5е (b) 2е 21

A: