AME $452-015,$ Spring $2023,$ HW$-4$

$4\mathrm{.}1$ The rod shown has a length of $0\mathrm{.}25$ m and is attached to the ground by a spring. The mass center is at the rod's geometric center. Assume $m=4kg,J=0\mathrm{.}02kg*m^2,k=40\frac{N}{m},$ and ${?}^{0}L=0\mathrm{.}08m.$

$($a$)$ Construct the mass matrix for the rod

$($b$)$ Determine the force of the spring

$($c$)$ Construct the $31$ array of applied forces $($do not include the weight$)$

$($d$)$ Construct and solve the equations of motion for the accelerations