The current I(t) in an LC series circuit is governed by the initial value problem below. Determine the current as a function of time t. 12 sin t, Osts2n I"(t) + 4(t) = g(t), I(0) = 1, I'(0) = 6, where g(t) =- 0, 2n

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Q: Let L(y(t)) = Y(s). The Laplace transform of another solution to the second-order differential…

A: Given solution is Ys = 5s2 +s -1s3 +9s  This can be written as Ys = 5s2 +s -1s s2 +9          = -19…

Q: Recall that the differential equation for the instantaneous charge g(t) on the capacitor in an…

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Q: Recall that the differential equation for the instantaneous charge q(t) on the capacitor in an…

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Q: fO volts, 0 < t <1 12 volts, x 2 1 which the resistance is 10 ohms and the capacitance is 0.32…

A: We are entitled to solve only one ques at a time. Please post another question separately. Given -…

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Q: 9. Which of the equations given below is the Laplace transform of the following differential…

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Q: The current I(t) in an LC series circuit is governed by the initial value problem below. Determine…

A: I"t+4It=gt,  I0=3, I'0=9, gt=3sint   , 0≤t≤2π0         ,  2π&lt;t   As  gt=3sint   , 0≤t≤2π0…

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Q: Consider the following initial-value problem. y" + 6y' + 10y = 8(t – 27), y(0) = 0, y'(0) = 0 Find…

A: We will find out the required solution using Laplace transform method.

Q: Consider the following initial value problem, in which an input of large amplitude and short…

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Q: Recall that the differential equation for the instantaneous charge q(t) on the capacitor in an…

A: We have to find q(t) and current i(t) using Laplace Transform Method by using Following Formulae,

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Q: Consider the initial value problem I' + 3r = 45t, r(0) = 2. a. Take the Laplace transform of both…

A: Given differential equation is x' +3x =45 t,   x0=2

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Q: 2. The position z(1) of a mass m on a spring with Hooke's constant k and damping constant y, subject…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

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Q: Recall that the differential equation for the instantaneous charge q(t) on the capacitor in an…

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Q: Recall that the differential equation for the instantaneous charge q(t) on the capacitor in an…

A: We have to find q(t) by using Following Laplace transform Formulae,

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Q: Use the Laplace transform to solve the following initial value problem: y" + 16y = 0, y(0) = 8,…

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Q: The current I(t) in an LC series circuit is governed by the initial value problem below. Determine…

A: Given that, l't+4lt=gt, . . .(1)  l0=3 , l'0=4 Where, gt=6sint , 0≤t≤2π0,         2π&lt;t The…

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Q: practice problem 2.1:  need help with what my A and phase angle would be for expression 7

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Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y'' -…

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Q: The current I(t) in an LC series circuit is governed by the initial value problem below. Determine…

A: Using Laplace transformation, the current as a function of time has been obtained.

Q: 2. Find the Laplace transform Y(s) of the solution y(t) of the initial value problem y"+4y=0,…

A: Apply Laplace transform on both sides

Q: 9. DETAILS ZILLDIFFEQMODAP11 7.3.034. Recall that the differential equation for the instantaneous…

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Q: Consider the following initial-value problem. y' - y = 2 cos(8t), y(0) = 0 Find L{f(t)} for f(t) = 2…

A: Leat=1s-a ; Lsin(at)=as2-a2; Lcos(at) =ss2-a2.

Q: Given this periodic function: f(t) =1 from 0<t<a and f(t) = 0 from a <t< 2a Solve for the Laplace…

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Q: Recall that the differential equation for the instantaneous charge g(t) on the capacitor in an…

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Q: Recall that the differential equation for the instantaneous charge q(t) on the capacitor in an…

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Q: Recall that the differential equation for the instantaneous charge g(t) on the capacitor in an…

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Q: Consider the following initial-value problem. y' y = 2 cos(7t), y(0) = 0 Find L{f(t)} for f(t) = 2…

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Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" -…

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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.