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K₁ ele 'W K₂ ell M₂ K3 ell
Transcribed Image Text:K₁ ele 'W K₂ ell M₂ K3 ell
Consider the mechanical system of the figure below, which consists of two masses M₁ =1 and M₂ = 2, each attached to a fixed base by a spring, having spring constants K1=1 and K3 = 2 respectively. The two masses are attached to each other by a third spring having constant K₂ = 2. When the system is released at time t = 0, M₁ is displaced 1 unit to the right of its equilibrium position and M₂ is displaced 2 units to the right of its equilibrium position, and their initial velocities are v₁ = 2 (moving towards right) and v₂ =-1 (moving towards left). Neglecting all frictional and damping effects, determine the positions of the masses at time t. Note: you must solve this problem using matrix method (eigenvalues and eigenvectors)
Transcribed Image Text:Consider the mechanical system of the figure below, which consists of two masses M₁ =1 and M₂ = 2, each attached to a fixed base by a spring, having spring constants K1=1 and K3 = 2 respectively. The two masses are attached to each other by a third spring having constant K₂ = 2. When the system is released at time t = 0, M₁ is displaced 1 unit to the right of its equilibrium position and M₂ is displaced 2 units to the right of its equilibrium position, and their initial velocities are v₁ = 2 (moving towards right) and v₂ =-1 (moving towards left). Neglecting all frictional and damping effects, determine the positions of the masses at time t. Note: you must solve this problem using matrix method (eigenvalues and eigenvectors)
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