# On the physical sample of “ discontinuous differential equations ”

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.)