Problem $3\mathrm{.}5$

What is the highest initial velocity that the $800$ lb machine can

have so that vibratory stress $($the stress caused by the vibration$)$

in each pad is less than $25\%$ of the yield stress? Each of the four

hollow Neoprene pads has an outer diameter of $4$ inches, an inner

diameter of $3\mathrm{.}5$ inches, a length of $2$ inches, a modulus of

elasticity of $1,500,$ and a yield strength of $2,000.$ Assume

the pads are neither stretched nor compressed initially.

Hint: The stress caused by an axial load is given by $=\frac{F}{A}$

where $F$ is the axial force in the bar and $A$ is the cross$-$sectional

area. Think about what vibratory system element the pads are and

how you can calculate the force in that element. Also think about how amplitude is related to displacement.

Answer: $43\mathrm{.}6i\frac{n}{s}$