Collaborative Problem $5\mathrm{.}1$

A continuously running machine $($weight $250$ lb $)$ is mounted on a steel plate as shown in the figure.

The machine generates a harmonic force at $40$ Hz with a magnitude of $420$ lb $.$ However, there is

too much vibration, so your manager has asked you to do something to reduce the amplitude of

vibration below $0\mathrm{.}01$ in$,$ preferably cheaply. There is a $2$ in thick piece of polymer padding left

over from something else you think might work if you center it under the steel plate $($also as shown

in the figure$).$

a$)$ Will your proposed design work?

b$)$ Does your proposed design increase or decrease vibration amplitude compared to no pad?