a) Derive the equations of motion for the system shown. Present the resulting equations in
matrix form.
b) If $x_3$ is held stationary, determine the natural frequencies of the system shown if
$m_1$=10kg, $m_2$=30kg, $k_1$=100N/m, $k_2$=500N/m, $c_1$=10Ns/m, and $c_2$=30Ns/m.
c) $x_3$ is suddenly subject to a step displacement of 0.1m 10 seconds later. Determine and
plot the displacement of the two masses.