Classical Mechanics Puzzler

Consider the solution to the simple pendulum of length L that is accelerated horizontally at constant rate a, that we solved in class. We found an equation of motion in the form,

Note that equilibrium occurs at angle q_o = - j .

Now consider the equation of motion for the standard non-accelerated simple pendulum, namely

and the equilibrium position is at q_o = 0.

Starting from non-acclelerated solution, describe how you could have come to the accelerated equation of motion by inspection. That is, what simple argument can you provide that explains why in the expression for w, g is replaced by (a² + g²) and the equilibrium position is at -j rather than zero.

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