Concept explainers
Vibrating Spring without Damping. A vibrating spring without dampening can be modelled by the initial value problem (11) in Example 3 by taking
a. If
b. After how many seconds will the mass in part (a) first cross the equilibrium point?
c. When the equation of motion is of the form displayed in
Example 3
In Section 4.1 we discussed the mechanics of the mass-spring oscillator (Figure 4.1, page 152), and we saw how Newton’s second law implies that the position
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Fundamentals of Differential Equations and Boundary Value Problems
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