Search Results for “brachistochrone”
Beat the Brachistochrone
You can drag the two green points to change the shape of the red track. Press play to watch a ball roll down the track and another ball roll down the straight line joining the end points. Experiment till you find the fastest track. Then press the Brachistochrone button to see the solution which Newton found. How close did you get to Newton's solution?
Cycloid is the Brachistochrone
The inverted cycloid is defined by rolling a circle below a horizontal line and tracing the locus of a point on its circumference. You can see the definition by animating theta. You can make the cycloid pass through point B by changing its radius. Now press the Play button to watch the ball roll along the cycloid. Compare its speed with a ball rolling down a straight line between A and B.
Tautochrone pendulum
By allowing the pendulum to wrap around a cycloid curve, we can constrain its mass to follow another cycloid (this, technically is because the evolute of a cycloid is a cycloid). As the cycloid is a tautochrone, the pendulums will have the same period no matter what their amplitude. Try dragging one mass close to horizontal, while leaving the other close to vertical. Do you observe that they have the same period?
