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Figs. (1) and (2) show how springs can be used to support a block in two different situations. In Fig. (1), they help decrease the amplitude of the fluctuating force transmitted by the block to the foundation. In Fig. $(2),$ they help decrease the amplitude of the fluctuating displacement transmitted by the foundation to the block. The ratio of the transmitted force to the impressed force or the ratio of the transmitted displacement to the impressed displacement is called the transmissibility. Derive an equation for the transmissibility for each situation. Give your answer in terms of the ratio $\omega_{f} / \omega_{n}$ of the frequency $\omega_{f}$ of the impressed force or impressed displacement to the natural frequency $\omega_{n}$ of the spring-mass system. Show that in order to cause any reduction in transmissibility, the ratio $\omega_{f} / \omega_{n}$ must be greater than $\sqrt{2}.$

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