The curves we will be looking at in this lab are cycloids. So let's review. I'll assume that you already know a little about cycloids, but let's go over what you'll be seeing. The first type of cycloid we will be examining is the linear cycloid. (Remember a cycloid is the path swept out by a point on a circle rolling along a path. In this case the path is a line.) A linear cycloid can be defined parameterically as
x(t) = a*t - b*sin(t)
y(t) = a - b*cos(t)
a, the absolute value of
b, and the shape of the cycloid? Draw or describe each of the three different cycloid shapes.
r = 1 + cos(theta)This can be defined parameterically as
x(t) = (1 + cos(t))*cos(t)
y(t) = (1 + cos(t))*sin(t)
Plot this curve and appreciate its beauty. If you do not you will be doomed to a life of misery and sorrow for this lost opportunity.