In Problems $39$ through $46,$ find the general solution of the system in Problem

$38$ with the given masses and spring constants. Find the natural frequencies of the

mass$-$and$-$spring system and describe its natural modes of oscillation. Use a computer

system or graphing calculator to illustrate the two natural modes graphically $($as in Figs.

$4\mathrm{.}2\mathrm{.}3$ and $4\mathrm{.}2\mathrm{.}4.$

$m_1=4,m_2=2,k_1=8,k_2=4,k_3=0$

$m_1=2,m_2=1,k_1=100,k_2=50,k_3=0$

$m_1=1,m_2=1,k_1=1,k_2=4,k_3=1$

$m_1=1,m_2=2,k_1=1,k_2=2,k_3=2$

$m_1=1,m_2=1,k_1=1,k_2=2,k_3=1$

$m_1=1,m_2=1,k_1=2,k_2=1,k_3=2$

$m_1=1,m_2=2,k_1=2,k_2=4,k_3=4$

$m_1=1,m_2=1,k_1=4,k_2=6,k_3=4$