Problem $5.$ Reconsider the mass$-$spring$-$dashpot. $(1)$ and $(2).$ Let $m_1=m_2=1kg,c_1=c_2=4k\frac{g}{s},k_1=0k\frac{g}{s^2},$ and $k_2=4k\frac{g}{s^2}.$ Use your answer from Problem $4$ to find the impulse response of $q_2(t)($i$.$c$.,$ the response where $u(t)$ is the delta function and all initial conditions are zero$).$ What happens to the position of mass $m_2$ as time tends to infinity?

Hint: $s^3+8s^2+24s+32=(s+4)(s^2+4s+8).$

$1$

$q,$

$q_2(t)$

Figure $1$: Two$-$degree$-$of$-$freedom mass$-$spring$-$dashpot system for Problem $4.$