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5. Do the following tasks using Mathematica

    For a Parametric curve  χ =  χ (t) , y = y(t) the curvature at a point p is:

(a) Parametric equations of the cycloid are:

     

(b)  Show that the curvature at top of any one of cycloid's arches  is 1/4.

       Hint: At top of any one of it's arches y is maximum 

(c)  Parametric equations of a circle of radius r are:

             

Show that the curvature of each point of a circle of radius r is K = 1/r

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5. Do the following tasks using Mathematica.

  1. Parametric equations of the cycloid are:

                        

Graph the cycloid for 0  ≤ θ ≤ 10  

  1. Show that the curvature at top of any one on cycloid’s aches is  

Hint: At top of any one of it’s arches y is maximum

  1. Parametric equations of a circle of radius r are:

                   

Show that the curvature of each point of a circle of radius r is 

 

Please upload the (.nb) file. 

    For a Parametric curve  χ =  χ (t) , y = y(t) the curvature at a point p is:

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