Monday, July 21, 2008

Answer: Inverted Pendulum
New Problem: Still Inverted Pendulum

Inverted Pendulum
Remember you want to swing the pendulum all the way up, but your eyes are closed so you don't know where the pendulum is. You do know that you want to add energy to the system. From rest, slide the bar a little to get things started. Then wait until you feel a tug, and pull in the opposite direction. That way you can ensure that the force you exert and the motion of the slider bar are the same direction, and therefore the work is positive; you're adding energy. If you were to move the slider in the direction it "wants" to go based on the tug you feel, the pendulum would be doing work on you, pulling your hand along for the ride.

Inverted Pendulum 2
We're going a bit more conceptual and less quantitative for a while to encourage more participation in the problem of the day, which had been fairly low for things like the planet formation problem. So the question is, think about the same apparatus as yesterday, but make the pendulum longer while keeping the mass the same. How is the task different? Easier, harder, or the same difficulty to balance the pendulum in the inverted position? Are the tugs you feel while swinging the pendulum bigger, smaller, or the same? How about the period of oscillations?

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