Chapter 4.P1, Problem 5P

Test the results of your design strategy for the situation described in Problem $4$ by performing several numerical simulations of Eq. $\left(\text{i}\right)$ in Problem $1$ using various values of $k$ as well as various input frequencies while holding the value of $\zeta$ fixed. For each simulation, plot the input $u\left(t\right)$ and the response $y\left(t\right)$ on the same set of coordinate axes. Do the numerical simulations support your theoretical results?

The vibrations in the floor of an industrial plant lie in the range $16-75\text{hertz}\left(\text{Hz}\right)$. The combined mass of the equipment and platform is $38\text{kg}$, and the viscous damping ratio of the suspension is $0.2$. Find the maximum value of the spring stiffness if the amplitude of the transmitted vibration is to be less than $10\%$ of the amplitude of the floor vibration over the given frequency range.

Eq. $\left(\text{i}\right)$ $y^{″}+2\zeta {\omega }_0{y}^{\prime }+{\omega }_0^{2}y=2\zeta {\omega }_0{u}^{\prime }+{\omega }_0^{2}u$.