Consider a simple harmonic oscillator resting on a roller belt, as shown in Figure. Assume...

Consider a simple harmonic oscillator resting on a roller belt, as shown in Figure. Assume that the frictional force exerted on the block by the roller belt depends on the slip velocity, , where u is the speed of the belt, and that it is given by

In other words, the force is constant when the slip velocity is outside the limits given by the constant v and is proportional to the slip velocity when it is within those limits.

(a) Write down the equation of motion for this oscillator. Solve it numerically, and make a phase-space plot for the following conditions: k = 1, m = 1, β = 5, v = 0.2, u = 0.1. Assume the following starting conditions.

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(b)

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(c)

Figure