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Differential Equation Matcher

Match the descriptions of physical processes to these differential equations.

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The Real Hydrogen Atom

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

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Differential Electricity

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

The Not-so-simple Pendulum 2

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
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.