The model mx'' + kx = 0 for simple harmonic motion, discussed in Section 5.1, can be related to Example 2 of this section.

Consider a free undamped spring/mass system for which the spring constant is, say, k = 10 lb/ft. Determine those masses m_n that can be attached to the spring so that when each mass is released at the equilibrium position at t = 0 with a nonzero velocity v₀, it will then pass through the equilibrium position at t = 1 second. How many times will each mass m_n pass through the equilibrium position in the time interval 0 < t < 1?