The position of an object in circular motion is modeled by the parametric equations x = 2 sin(2t) cos(2t) where is measured seconds_ (a) Describe the Path of the object by stating the radius of the circle the pasition at time counterclockwise), and the time it takes to complete one revolution around the circle. the arientation pf motion (clockwise or The radius is the position at time t = 0 is (X, Y) = 0,2 and the motion is clockwise It takes units of time to complete one revolution. (b) Suppose the speed of the object doubled: Find new parametric equations that model the motion of the object: (x(t) , v(t)) = Sin ( 4t),2 cOS (c) Find rectangular-coordinate equation for the same curve by eliminating the parameter: Find polar equation for the same curve_ (Use variables and needed: )

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ShubhamSrivastava ShubhamSrivastava · Answer 1 · 2022-12-13T11:05:39-05:00

The object defined as trigonometric function is rotating clockwise and has a radius of 2 units completing one revolution in π seconds

The path followed by the object is a circular one as;

r=[tex]\sqrt{4sin^2 2t+4cos^2 2t\\}[/tex] = [tex]\sqrt{4*1\\}[/tex] = 2 which is the radius of the circle.

The motion is clockwise +ve.

Time taken to complete one revolution= 2π/2 rad per second= π seconds.

If the speed of the object is doubled:

Linear velocity= ωr = 4 units/s

New Linear velocity after doubling= 8m/s

New angular velocity= [tex]\frac{8}{2\\}[/tex] rad/s= 4 rad/s

To find rectangular coordinate;

Sin2t= [tex]\frac{x}{2\\}[/tex] Cos2t= [tex]\frac{y}{2}[/tex]; [tex]sin^{2} 2t + cos^{2} 2t[/tex]=1

Hence [tex]x^{2} +y^{2}\\[/tex]= 4

Substituting the values of t the polar coordinates are (0,2) and (0,-2)

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