Search Results for “springs”
Pendulum Spring Mass
A simple chaotic mechanism comprising a pendulum attached by a spring to a mass which is free to slide horizontally.
A Three Body Problem
Three masses are joined by springs and let loose on a horizontal, frictionless plane. You can reposition the masses by dragging, if you can catch them.
A Chaotic Flywheel
The left hand flywheel is driven at a constant velocity. The right hand wheel is connected by a spring, whose natural length is equal to the distance between the centers of the flywheels, and whose stiffness is k. Output is the angle (in radians) of the flywheel. Note that when k is approximately 5, the motion is regular. Try different values of k, and observe the onset of chaos.
Symmedian Point
Lets take 3 stretched springs attached to the sides of a triangle (in such a way that they can slip along the lines). These will be ideal springs with 0 natural length. Attach all 3 to a mass D, where will it end up? Press Show to see the geometric answer. (Grey lines are medians, purple lines are angle bisectors, and yellow lines are the reflections of the medians in the angle bisectors.) Now, can you work out why?
Regiomontanus Problem
We seek the place on the earth's surface where a vertically suspended bar (or the rings of Saturn) look the biggest. A machine to solve this problem consists of a mass fixed to the earth's surface and a couple of bars attached to the mass and constrained to pass through the ends of the bar. A spring between the bars pushes them apart. The machine reaches equilibrium when the bars are as far apart as possible, hence finding the solution to Regiomontanus' Problem. You can drag the ends of the bar to change the problem. Press Show to see the circumcircle of the ends of the bar and the mass. You should notice something about the position of this circumcircle at equilibrium. Can you explain what you have noticed?
Two ways of finding the Fermat Point
This simulation finds the Fermat point as the equilibrium position of the knot in 3 pieces of string, and as the intersection of the perpendiculars to a spring loaded equilateral triangle. Try dragging the corners of the yellow triangle.
Least Square Linear Regression
Move the points then press the play button. The potential energy of the (zero natural length) springs is proportional to the sum of their length. Equilibrium will occur when the regression line is found
Drive in Movie Problem
This machine computes the best location to view a drive in movie (maximizes the angle). The machine is composed of a pair of mechanical jaws attached at the ends to the top and bottom of the screen and at the middle to the viewing plane. The jaws are pushed apart by a compressed spring, which will find equilibrium when the jaws are as far open as possible..
