Chapter 11: Problem 2
A massless spring (force constant \(k_{1}\) ) is suspended from the ceiling, with a mass \(m_{1}\) hanging from its lower end. A second spring (force constant \(k_{2}\) ) is suspended from \(m_{1}\), and a second mass \(m_{2}\) is suspended from the second spring's lower end. Assuming that the masses move only in a vertical direction and using coordinates \(y_{1}\) and \(y_{2}\) measured from the masses' equilibrium positions, show that the equations of motion can be written in the matrix form \(\mathbf{M y}=-\mathbf{K y},\) where \(\mathbf{y}\) is the \(2 \times 1\) column made up of \(y_{1}\) and \(y_{2} .\) Find the \(2 \times 2\) matrices \(\mathbf{M}\) and \(\mathbf{K}\).
Short Answer
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Key Concepts
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