Problem $6\mathrm{.}2$

A $135$ lb washing machine is supported by four circular pads. Each pad has an elastic modulus of $800$ psi $,$ a height of $2\mathrm{.}5$ inches, and a diameter of $1\mathrm{.}25$ inches. The machine primarily vibrates side to side. Assume the damping ratio of the system is $0\mathrm{.}11.$ A $13$ lb $($when wet$)$ blanket is being washed. The blanket can be modeled as a point mass $15$ inches from the center of rotation. Suppose the washing machine is spinning at $550$ rpm $.$

a$)$ Find the amplitude of vibration.

b$)$ Find the amplitude of the force transmitted to the ground.

c$)$ Will the washing machine shake more or less if it spins faster? Justify your answer.