As a model of a linear triatomic molecule (such as CO). consider the system shown in...

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As a model of a linear triatomic molecule (such as CO₂). consider the system shown in Figure 11.21, with two identical atoms each of mass m connected by two identical springs to a single alom of mass M. To simplify matters, assume that the system is confined to move in one dimension. (a) Write down the Lagrangian and find the normal frequencies of the system. Show that one of the Ommmm P₁ mome Figure 11.21 Problem 11.32 B normal frequencies is zero. (b) Find and describe the motion in the normal modes whose frequencies are nonzem. (c) Da the same for the mode with zero frequency. Iffint: See the comments at the end of Problem 11.27.1 As a model of a linear triatomic molecule (such as CO₂). consider the system shown in Figure 11.21, with two identical atoms each of mass m connected by two identical springs to a single alom of mass M. To simplify matters, assume that the system is confined to move in one dimension. (a) Write down the Lagrangian and find the normal frequencies of the system. Show that one of the Ommmm P₁ mome Figure 11.21 Problem 11.32 B normal frequencies is zero. (b) Find and describe the motion in the normal modes whose frequencies are nonzem. (c) Da the same for the mode with zero frequency. Iffint: See the comments at the end of Problem 11.27.1

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