Two masses (m_{1}) and (m_{2}), each connected by two springs of stiffness (k), are connected by a

Question:

Two masses $m_{1}$ and $m_{2}$, each connected by two springs of stiffness $k$, are connected by a rigid massless horizontal rod of length $l$ as shown in Fig. 5.22.

(a) Derive the equations of motion of the system in terms of the vertical displacement of the C.G. of the system, $x(t)$, and the rotation about the C.G. of the system, $\theta(t)$.

(b) Find the natural frequencies of vibration of the system for $m_{1}=50 \mathrm{~kg}, m_{2}=200 \mathrm{~kg}$, and $k=1000 \mathrm{~N} / \mathrm{m}$. Assume $l=1 \mathrm{~m}$.

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