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Differential Equation Matcher

Match the descriptions of physical processes to these differential equations.

The Real Hydrogen Atom

Dip your toe into the world of quantum mechanics by looking at the Schrodinger equation for hydrogen atoms

Differential Electricity

As a capacitor discharges, its charge changes continuously. Find the differential equation governing this variation.

The Not-so-simple Pendulum 2

Age 16 to 18 Challenge Level:
Intuitively, how does friction affect motion? Does the $v$ term accomplish this to some level?

How does the equation relate to $F=ma$?

As a rough sketch without any calculation, what would you expect the trajectory over time of the exact, real pendulum motion be over time? Compare this to a plot of the solution. What would be realistic values of the parameters? Make some well-reasoned estimations if you have no intuitive sense for the scale of the parameters.