,

so

From conservation of energy: ,

, so

However, from an intermediate point ,

So

with

define

So the amount of time is the same from any point.

1. A cycloid is the curve defined by the path of a point on the edge of circular wheel as the wheel rolls along a straight line.

2. Cycloidal curves is the curve of fastest descent under gravity

3. the period of a ball rolling back and forth inside this curve does not depend on the ball’s starting position./htdocs/ntnujava/ejsuser/2/users/ntnu/fkh/cycloids_pkg/cycloids.propertiesFull screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list

Download EJS jar file(1359.7kB):double click downloaded file to run it. (20 times by 12 users) , Download EJS source (10 times by 7 users) View EJS source