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The following source contains several physical examples: https://arxiv.org/pdf/0901.3583.pdf.

How can I get the differential equation in "Example 2: Brick on a frictional ramp"? How can I grasp this as a math student?

$$ \dot{v}(t) = g(\sin \theta) − \nu g(\cos \theta) \text{sign}(v(t)) $$

Moreover, do you think there is a physical form of the equation in "Example 3: Non-smooth harmonic oscillator"? (like exp 2.)

Thank you very much in advance for your answers.

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