e current I(t) in an LC series circuit is governed by the initial value problem below. Determine the rrent as a function of time t. 63 sin 2t, 0st<2r I"(t) + 251(t) = g(t), I(0) = 2, I'(0) = 36, where g(t) = 0, 2n

Q: 00 1. Find the laplace transform of, f(t) =sin(t +a)cos(t -a) using e-stf(t)dt.

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Q: A function f(t) is defined by f(t) = 4 0<t <3 = 2t + 1 3 ≤t. Sketch the graph of the function and…

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Q: Q1/ Find the laplace transform for the following 1 - e-6t sin(10t-8)

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Q: Use the Laplace transform to solve the given initial-value problem. y' - y = 2 cos(9t), y(0) = 0…

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Q: When calculing the Laplace transform of the function f(t)=e^2t.sin(4t) is obtained as a result:

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Q: From a Laplace Transform form, we have the following expressions: s - w I) L{ewt cos(ßt)} (s – w)2 +…

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Q: i). ƒ (1) = (5– 312) ² i). ƒ (1) =r2sinh (21) Find the Laplace transforms of the following…

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Q: Find the Laplace transform of the following functions: 1. L{5} 2. L{t³} 3. L{e³t} 4. L{sin 4t} 5.…

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Q: - Find the Laplace transform of the following functions. (a) f(t) = e 2t-3 sin(2t) + ²t cos(3t) sint…

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Q: Find the Laplace transform F(s), given that f(t) is: (a) 2tu(t – 4) (b) 5 cos(t) 8(t – 2)

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Q: 2. Y(s) = J(2s – 3)5 %3D

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Q: Compute the Laplace transform. Your answer should be a function of the variable s L{3+ u(t)e sin(7…

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Q: find the Laplace transform of VE cos(3Vf). E{VE cos(3V)} =0.

A: We are given that,  Lcos3tπt=e2.25ss..................................................(1) We are…

Q: b) f(t) = 3 sin(2t) + 5e³t so

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Q: -t sin 4t -t sin 4t

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Q: Wt = 7' wzz, -00 0 w(x, 0) = 3 sin(6x) using the Laplace transform. First if we let W(x, s) = W(x)…

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Q: 2) Sketch the graph of the following s functions and find the Laplace transfo a) f1(t) = }4 – t, (o,…

A: Given,      (a)    f1(t)=t0≤t&lt;24-t2≤t&lt;40t≥4      (b)    f2(t)=00≤t&lt;1t1≤t&lt;21t≥2

Q: 7. Graph the function f(t)=2U(t-1)-3U(t-2) and find its Laplace Transform 8. Write the function…

A: Remark : As per new guildline,  in case  of posting multiple question we will answer of only first…

Q: (D² + 2D- 3)y = sin 2x; y(0) = y'(0) = 0 (Use The Laplace Transform)

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Q: 5.) f(t) = cos (mt) u (7-2)

A: Laplace transform of the function

Q: 3. Find CH(t) when H(t) = (et-3)(e?-) %3D

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Q: Using only the Laplace transform table to obtain the Laplace transform of the following functions:…

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Q: ®[6.4] Using the Laplace transform to solve IVP. yu t16y= 43(t-37) H10)=2 , y'0) =0 y10)%=D2 %3D 3D0

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.