5. Consider the undamped forced mechanical system mu" + 16u = cos wt, (a) For what values of the mass m will this system exhibit a resonance if w = 2? (b) Write down the general solution to this nonhomogeneous equation with the ma m found in (a). (c) Let u(0) = 0 and u'(0) = 0 for (b). Find the solution of the initial value problen Based on the solution you obtain, explain what happens when t increases an what happens when t → ∞.

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A: The matrix form of the given system of differential equations is x^'=Ax^, with A=r33r, x^=xy.

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Q: Consider the initial value problem (r + 1)y" – y" – (x + 1)y' + y = 0 y(0) = 2, y(0)' = 1, y(0)" = 1…

A: Let us consider a differential equation an(x)y(n)+a2(x)y(n-1)+a3(x)y(n-2)+.......+a1(x)y'+a0(x)y=0…

Q: Please I want solve this question

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Q: 2.9. (a) Solve the integral .. (dx.draw) 3N and use it to determine the "volume" of the relevant…

A: V3w=∫0≤∑i=13Nxi≤R∫ (dx1,…dx3N) Obviously, the volume vn will be propositional to Rn

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A: since you have posted multiple question in this question which are not interlinked so i have solved…

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Q: In the Laplace (or potential) equation: ux + Uyy = 0, the solutior u(x, y), which represerts…

A: Given, uxx+uyy=0, 0≤x≤1, 0≤y≤2....1 With boundary conditions, ux,0=0, ux,2=x1-x, 0<x<100,y=0,…

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Q: (2 ) Consider the following system of differential equation, with time domain te (0,1): x' = -2x +…

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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.