Q4/A/ The mechanical system consists of two bodies of mass 1 on three springs of the same spring constant k and of negligibly small masses of the springs. Also damping is assumed to be practically zero. Then the model of the physical system is the system of ODES. 1 y"₁ = -ky₁+k(y₂ - Y₁) -k(y₁ - y₁)-k y₂ y"₂ 2 We shall determine the solution corresponding to the initial conditions y₁ (0) = 1, y₂ (0) = 1, y₁ (t) y'₁ (0) = √3k, and y'₂ (0) = -√3k. Use the Laplace transform method to find and y₂ (t). =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Q4/A/ The mechanical system consists of two bodies of mass 1 on three springs of the same spring
constant k and of negligibly small masses of the springs. Also damping is assumed to be practically
zero. Then the model of the physical system is the system of ODES.
1
y"₁ = -ky₁+k(y₂ - Y₁)
-k(y2-y₁)-k y2
y"₂
2
We shall determine the solution corresponding to the initial conditions y₁ (0) = 1, y₂ (0) = 1,
y'₁(0) = √3k, and y',(0) = -√3k. Use the Laplace transform method to find y₁ (t)
and y₂ (t).
=
Transcribed Image Text:Q4/A/ The mechanical system consists of two bodies of mass 1 on three springs of the same spring constant k and of negligibly small masses of the springs. Also damping is assumed to be practically zero. Then the model of the physical system is the system of ODES. 1 y"₁ = -ky₁+k(y₂ - Y₁) -k(y2-y₁)-k y2 y"₂ 2 We shall determine the solution corresponding to the initial conditions y₁ (0) = 1, y₂ (0) = 1, y'₁(0) = √3k, and y',(0) = -√3k. Use the Laplace transform method to find y₁ (t) and y₂ (t). =
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