Chapter 5.6, Problem 10E

Suppose the coupled mass-spring system of Problem 1 (Figure 5.31) is hung vertically from a support (with mass $m_2$ above $m_1$), as in Section 4.10, page 226.

a. Argue that at equilibrium, the lower spring is stretched a distance $l_1$ from its natural length $L_1$, given by $l_1=m_{1}g/k_1$.

b. Argue that at equilibrium, the upper spring is stretched a distance $l_2=\left(m_1+m_2\right)g/k_2$.

c. Show that if $x_1$ and $x_2$ are redefined to be displacements from the equilibrium positions of the masses $m_1$ and $m_2$, then the equations of motion are identical with those derived in Problem 1.