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Two equal masses m are constrained to move without
Chapter 11, Problem 11.18(choose chapter or problem)
Two equal masses m are constrained to move without friction, one on the positive x axis and one on the positive y axis. They are attached to two identical springs (force constant k) whose other ends are attached to the origin. In addition, the two masses are connected to each other by a third spring of force constant \(k^{\prime}\). The springs are chosen so that the system is in equilibrium with all three springs relaxed (length equal to unstretched length). What are the normal frequencies? Find and describe the normal modes.
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QUESTION:
Two equal masses m are constrained to move without friction, one on the positive x axis and one on the positive y axis. They are attached to two identical springs (force constant k) whose other ends are attached to the origin. In addition, the two masses are connected to each other by a third spring of force constant \(k^{\prime}\). The springs are chosen so that the system is in equilibrium with all three springs relaxed (length equal to unstretched length). What are the normal frequencies? Find and describe the normal modes.
Step 1 of 9
The Lagrangian equation of the system is given by,
\(L=T-U\)
Here, T is kinetic energy of the system, and U is the potential energy.
If the Lagrangian function of a system is \(L=f\left(q_{1}, q_{2}, \ldots, q_{i}\right)\) the, the Lagrangian equation of motion is given by,
\(\frac{d}{d t}\left(\frac{\partial L}{\dot{\partial} q}\right)=\frac{\partial L}{\partial q}\)
Draw the schematic arrangement of two equal masses as follows.
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