H.W-7 Applications of simultaneous Differential Equations k The system shown in figure begins to move under the following M₁ initial conditions: initial displacement X1(0) = 1 cm, x2(0) = 1 cm, initial velocity x'1(0) = = √√3km, x'2(0)=√3k cm/sec. neglecting ст sec' friction, derive and solve the differential equations governing the free vibration of the system. Knowing that M₁ =M2 =1(N.sec²/cm). k k M2 X1 X2

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H.W-7 Applications of simultaneous Differential Equations
The system shown in figure begins to move under the following
initial conditions: initial displacement x1(0) = 1 cm, x2(0) = 1 cm,
initial velocity x'1(0) = √3km, x'2(0) = -√3k cm/sec. neglecting
cm
sec
friction, derive and solve the differential equations governing the
free vibration of the system. Knowing that M₁ M₂ =1(N.sec²/cm).
k
m M₁
k
m
=↑
M₂
X2
k
Transcribed Image Text:H.W-7 Applications of simultaneous Differential Equations The system shown in figure begins to move under the following initial conditions: initial displacement x1(0) = 1 cm, x2(0) = 1 cm, initial velocity x'1(0) = √3km, x'2(0) = -√3k cm/sec. neglecting cm sec friction, derive and solve the differential equations governing the free vibration of the system. Knowing that M₁ M₂ =1(N.sec²/cm). k m M₁ k m =↑ M₂ X2 k
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