Q1: find the Laplace transform of the following? dy dt ди( у,1) 2 ди(у,1) ây 3

Q: Find the Laplace transform of f(t) t sin(2t) dr F(s) =

A: We use the table of Laplace transform to solve the given question.

Q: (a) f(t) = cosh² t (b) f(t) = 2 sinh? 2t 2

A: To find the Laplace transforms of the given functions we will use the following table of Laplace…

Q: 120. 00 L{f(t)} = 6. e-stf(t) dt d to be the Laplace transform of f, prov

A: Given: f(t)=0, t<1t, t≥1 from the graph of f(t)

Q: f(t)= t³ cost

A: 8

Q: Q3) If f(t) tsin(at) then its Laplace Transform is given by? %3D a) 2as/(s²+a²)² b) a/s²+a? c)…

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Q: * Q5- Find the Laplace transform for f(t) = ( e5t + sin t )²

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Q: y" + 4y = 5e-t, y(0) = 2, y'(0) = 3. Take the Laplace transform of the above, and solve for Y(s).

A: Differential equations are those equations of mathematics that involve dependent variables ,…

Q: Q4) Iff(t) = eat, its Laplace Transform is given by? %3D a) a/s²+a² b) VT/2vs c) 1/s-a d) Does not…

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Q: Find the Laplace transform of: f (t) = cos? 2t

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Q: Find the Laplace transform of 0, 0, t < 4 f(t) = l12 – 8t + 22, t24 -

A: Laplace transform of pice wise function

Q: 5. What is the Laplace Transform of f(t) = t° cos h 2t? (42) b) 3/

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Q: TT f(t) = 10 cos(t 6,

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Q: Find the Laplace transform of f(t)=∫t0τsin(2τ) dτ

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Q: HW Q. 2 - Derive the Laplace transform of f (t) = sinh(at)

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Q: f(t)= 5 cos? 2t

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Q: f(t) dt3 cos 2t

A: Sol:- First find the derivative d3dt3cos2t=d2dt2-sin2t· 2=ddt-4cos2t=8sin2t

Q: Find the Laplace transform of f (t) = e2t * cost %3D (S+2)(S²+1) (S+2)(S2+1) the above

A: Solution: The objective is to find the Laplace transform of the given function

Q: b. f(t) = e-04t cos12t

A: Solution

Q: Find the Laplace transform of f(t) = 5e−2t − 3   sin(4t), t ≥ 0.

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Q: Find the Laplace Transform of f(t)= e"(2cosh 2t + sinh t). %3D 2s+3 A) f(s) = %3D s2-4s-5 2s-3 f(s)…

A: Le2t2cosh2t+sinhtApply transform rule:  if Lft=Fs then  Leatft=Fs-a.For e2t2cosh2t+sinht:…

Q: f(t) = (3t – 5)e²". %3D What is the Laplace Transform of f'(1)?

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Q: se the Convolution Theorem to find the Laplace Transform of f (t) = S, et-T sin 2rdT.

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Q: determine the Laplace transform of f. Q. f(t)=2e3t sint +4e−t cos3t.

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Q: Find the laplace transform of (a) f(t) = 4t3 – 2t2 + 5 %3D (b) f(t) = tcosh2t + t?sin5t + t3

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Q: What is the Laplace transform of: f(t)=5t+18+41²H(t-6)?

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

Q: sin 2t, Find the Laplace transform of f(t) = 0, 0 <t<T by using the second shifting property.

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Q: 8. Find the Laplace transform of 0, f(t) = t 4.

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Q: Find the Laplace transform of f(t) = e4t + 7sin(2t).

A: We will use the formula Lf(t) = F(s)Leat = 1s-a                    Lsin at = as2+a2

Q: I t los 2t e-を

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Q: f(t)=e'(4 e2" + 5)?.

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Q: If y " +3y +9y = 6e-3t, y (0) = 0, y (0) = 5 what is the Laplace transform of y? %3D

A: Given Solve using Laplace y''+3y'+9y=6e-3t, y0=0, y'0=5

Q: ) Find the Laplace transform of t 2 F(s) =

A: In the given question we have to find the Laplace transformation of the given piecewise function. In…

Q: Find the Laplace transform of f()= et sin(6 t)+9. 4. 6. F(s) = (s-4)2+ 16 s? F(s)= (s- 4)? + 36 %3D…

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Q: If the Laplace Transform of F (t) = vi what is the Laplace Transform of is 4s 2 F (t) = e' vt3?

A: Laplace transform of F(t) = et root t3

Q: ,determine the Laplace transform of f. Q. f(t)=e−2t sin(t −π/4).

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Q: solve for the laplace transform f(t) = {t,t

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Q: y(t) = 5e2 cos(3t) + te-3t %3D

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Q: What is the laplace transform of f(t) = e5tsint?

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Q: What is the laplace transform of f(t)= t4 e³t

A: Solution

Q: -24 e Fis)= ?

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Q: Find the Laplace transform of f(t) = u(t – 4) · e' F(s) %3D 8-2

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Q: Find the Laplace transform of: f (t) = v1+ sin t + (7t)14 + t² sin 2t

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Q: If the Laplace Transform of F (t) = Vt3 is 3 T , what is the Laplace Transform of 5 4s 2 F (t) = e'…

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Q: O Find the Laplace transform of e³ + 2tª – 4 cos 8t + ez + Vt3

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Q: Prob.23. Calculate the Laplace transform of the following – (i) t" 1-e' (ii) (iüi) t sin at

A: Given that 1- t^n Laplace transform of t^n will be We know that L(t^n) = n!/s^(n+1)…

Q: Q6 de +y = Cos(t), y(0) = 0, y'(0) = -1, Use Laplace Transform.

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Q: Find the Laplace transform of f(t) = e='(t² + 3t + 4)

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Q: Find the Laplace transform of (ii) tJj(t). (i) J,(t),

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Q: Find the Laplace transform of (a) fC) = sin 2 (t +) (b) (c) (d) f(t) = (sint – kos t)? f(t) = kos²…

A: Note: Our guidelines we are supposed to answer only first three subpart . Kindly repost other…

Q: Show that the Laplace Transform of Cosh(wt) %3D s2-w?

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