Waves and Oscillations - Two Coupled Masses : Normal Modes of Transverse Oscillations
A system consisting of three identical springs and two equal masses may oscillate in transverse mode. In this case the differential equations of motion are solved and the normal modes of oscillations are found under two approximations- Slinky approximation and Small-oscillation approximation. In the slinky approximation, the frequencies of the normal modes of transverse oscillations are same as those of longitudinal oscillations. In the small-oscillation approximation, the oscillating parts of the system stay close to the equilibrium position. The mode frequencies of the transverse small oscillations are smaller than their corresponding frequencies of the longitudinal small oscillations.
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