# Matrix equation of motion

1) For the two degree of freedom structure shown:

i) what is the matrix equation of motion?. Assume that m1 and m2 oscillate harmonically with the same frequency but with different amplitudes X1 and X2 of x1(t) and x2(t).

ii) what are the values of the amplitude ratios r1 and r2

if m1 = m2 = m, k1 = k, and k2 =3k?

See attached file for full problem description.

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#### Solution Summary

Using a provided degree of freedom structure, the solution explains what the matrix equation of motion is and what the value of the amplitude rations r1 and r2 are.

Matrix Form: Inhomogeneous Differential Equations

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(see the attachment for the full question)

x = -2x - y + 12t + 12,

y = 2x - 5y - 5

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I have another problem below but on a similar topic:

If an object moves in the plane in such a way that its Cartesian coordinates (x, y) at time t satisfy the following homogeneous system of second-order differential equations:

x = -2x - y,

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Express the system in matrix form?

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