Sticky Friction. An alternative for the damping friction model
Figure
(The function sign(s) is
Thus, if the mass is at rest, friction balances the spring force if
a. Taking
b. Form the phase plane equation for (17) when
where the plus sign prevails for
c. Identify the trajectories in the phase plane as two families of concentric semicircles. What is the center of the semicircles in the upper half-plane? The lower half-plane?
d. What are the critical points for (17)?
e. Sketch the trajectory in the phase plane of the mass released from rest at
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Fundamentals of Differential Equations and Boundary Value Problems
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