Contemplate a setup involving a pair of toy mine cars (assumed to have no friction) joined by two springs. One of these springs is fastened to a wall, as depicted in the diagram. Let's denote the displacements of the first and second masses from their balanced points as "x," and "x₂," respectively. Given that the masses are M₁ = 8 kg and M₂ = 4 kg, and the spring constants are k, = 256 N/m and k₂ = 128 N/m, 1 2 Lumm mi monito K2 DETERMINE THE SYSTEM OF SECOND ORDER DIFFERENTIAL EQUATIONS FOR THE SYSTEM OF MINECARS AND THEN FIND THE GENERAL SOLUTION TO THIS SYSTEM OF DIFFERENTIAL EQUATIONS USING A,,A2,B1,B2 to denote any arbitrary constants. General solution: x, (t) = X₂ (t)= Lum Second order differential equation: *==

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Contemplate a setup involving a pair of toy mine cars
(assumed to have no friction) joined by two springs. One of
these springs is fastened to a wall, as depicted in the diagram.
Let's denote the displacements of the first and second masses
from their balanced points as "x," and "x₂," respectively. Given
that the masses are M₁ = 8 kg and M, = 4 kg, and the spring
constants are k, = 256 N/m and k₁₂ = 128 N/m,
1
2
Mi
DETERMINE THE SYSTEM OF SECOND ORDER
DIFFERENTIAL EQUATIONS FOR THE SYSTEM OF MINECARS
AND THEN FIND THE GENERAL SOLUTION TO THIS SYSTEM
OF DIFFERENTIAL EQUATIONS USING A,,A2,B1,B2 to denote
any arbitrary constants.
x₁ (t) =
Lumm
Kz
Second order differential equation:
"X"=
3
General solution:
X₂ (t)=
Transcribed Image Text:Contemplate a setup involving a pair of toy mine cars (assumed to have no friction) joined by two springs. One of these springs is fastened to a wall, as depicted in the diagram. Let's denote the displacements of the first and second masses from their balanced points as "x," and "x₂," respectively. Given that the masses are M₁ = 8 kg and M, = 4 kg, and the spring constants are k, = 256 N/m and k₁₂ = 128 N/m, 1 2 Mi DETERMINE THE SYSTEM OF SECOND ORDER DIFFERENTIAL EQUATIONS FOR THE SYSTEM OF MINECARS AND THEN FIND THE GENERAL SOLUTION TO THIS SYSTEM OF DIFFERENTIAL EQUATIONS USING A,,A2,B1,B2 to denote any arbitrary constants. x₁ (t) = Lumm Kz Second order differential equation: "X"= 3 General solution: X₂ (t)=
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