The variables x (t) and x(t) represent the positions of mass m, and m. The force...

 

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The variables x₁ (t) and x₂(t) represent the positions of mass m, and m₂. The force f(t) is the system input, whilst the output is the position x₂(t). Here the masses are m₁ = 1 kg and m₂ = 1 kg and the damper b= 1 Ns/m. The spring is nonlinear, and the force (N), F(t), required to stretch the spring is: F(t) = 2x² (t) Eq.(1) Using a free-body-diagram, show that the differential equations representing the system in Figure 1 are given by: d²x₁ (t), dx, (t) dt + dt² + 2x²(t) d²x₂ (t) dx₂(t) + dt² dt dx₂ (t) dt dx₁ (t) dt = 0 = f(t) Eq.(2) Eq.(3) -X₁ (1) H Figure 1: Nonlinear mass-spring-damper system Fs - 0000 m1 -X₂(1) m? f) The variables x₁ (t) and x₂(t) represent the positions of mass m, and m₂. The force f(t) is the system input, whilst the output is the position x₂(t). Here the masses are m₁ = 1 kg and m₂ = 1 kg and the damper b= 1 Ns/m. The spring is nonlinear, and the force (N), F(t), required to stretch the spring is: F(t) = 2x² (t) Eq.(1) Using a free-body-diagram, show that the differential equations representing the system in Figure 1 are given by: d²x₁ (t), dx, (t) dt + dt² + 2x²(t) d²x₂ (t) dx₂(t) + dt² dt dx₂ (t) dt dx₁ (t) dt = 0 = f(t) Eq.(2) Eq.(3) -X₁ (1) H Figure 1: Nonlinear mass-spring-damper system Fs - 0000 m1 -X₂(1) m? f)

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This shows a diagram of a nonlinear massspringdamper system We will explain more about it below The ... View the full answer