boundary-value

Harmonic Motion

Simple Harmonic Motion 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 mn 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 mn pass through the equilibrium position in the time interval 0 < t < 1?

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