a marble is rolled on the floor in a straight line from one person to another person. the marble has a…

a marble is rolled on the floor in a straight line from one person to another person. the marble has a radius of 0.9 cm and there is a fixed point ( p ) located on the marble. let the person rolling the marble represent the origin. find parametric equations in terms of ( \theta ) describing the cycloid traced out by ( p ).

a marble is rolled on the floor in a straight line from one person to another person. the marble has a radius of 0.9 cm and there is a fixed point ( p ) located on the marble. let the person rolling the marble represent the origin. find parametric equations in terms of ( \theta ) describing the cycloid traced out by ( p ).

Answer

Explanation:

Step1: Recall the parametric equations for a cycloid

The parametric equations for a cycloid generated by a circle of radius (r) are (x = r(\theta-\sin\theta)) and (y=r(1 - \cos\theta)), where (\theta) is the angle of rotation of the circle.

Step2: Substitute the radius value

Given that (r = 0.9) cm. For the (x) - coordinate: (x=0.9(\theta-\sin\theta)) For the (y) - coordinate: (y = 0.9(1-\cos\theta))

Answer:

The parametric equations are (x = 0.9(\theta-\sin\theta)) and (y=0.9(1 - \cos\theta))