Four rigid bodies, 1, 2, 3, and 4, are connected by four springs as shown in the

Question:

Four rigid bodies, 1, 2, 3, and 4, are connected by four springs as shown in the figure. Bodies 2 and 4 are fixed. Assume the bodies can undergo only translation in the horizontal direction. The spring constants ( $\mathrm{N} / \mathrm{mm})$ are: $k_{1}=400, k_{2}=500, k_{3}=500$, and $k_{4}=300$. Assume the mass of bodies 1 and 3 as $m_{1}=10 \mathrm{~kg}, m_{3}=30 \mathrm{~kg}$. Calculate the natural frequencies and corresponding mode shapes.

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