Chapter 7.10, Problem 22E

Recompute the coupled mass-spring oscillator motion in Problem 1, Exercise 5.6 (page 287), using the Laplace transforms.

1. Two springs and two masses are attached in a straight line on a horizontal frictionless surface as illustrated in Figure 5.31. The system is set in motion by holding the mass $m_2$ at its equilibrium position and pulling the mass $m_1$ to the left of its equilibrium position a distance $1\text{m}$ and then releasing both masses. Express Newton’s law for the system for the system and determine the equations of motion for the two masses if $m_1=1\text{kg}$, $m_2=2\text{kg}$, $k_1=4\text{N}/\text{m}$, and $k_2=10/3\text{N}/\text{m}$.