In this section we stated that parametric equations contain more information than just the shape of the curve. Write a short paragraph explaining this statement. Use the following example and your answers to parts (a) and (b) below in your explanation. The position of a particle is given by the parametric equations x = sin(t) and y represents time. We know that the shape of the path of the particle is a circle. cos(t) where t a) How long does it take the particle to go once around the circle? Find parametric equations if the particle moves twice as fast around the circle. b) Does the particle travel clockwise or counterclockwise around the circle? Find parametric equations if the particle moves in the opposite direction around the circle.
In this section we stated that parametric equations contain more information than just the shape of the curve. Write a short paragraph explaining this statement. Use the following example and your answers to parts (a) and (b) below in your explanation. The position of a particle is given by the parametric equations x = sin(t) and y represents time. We know that the shape of the path of the particle is a circle. cos(t) where t a) How long does it take the particle to go once around the circle? Find parametric equations if the particle moves twice as fast around the circle. b) Does the particle travel clockwise or counterclockwise around the circle? Find parametric equations if the particle moves in the opposite direction around the circle.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:In this section we stated that parametric equations
contain more information than just the shape of the
curve. Write a short paragraph explaining this
statement. Use the following example and your
answers to parts (a) and (b) below in your
explanation.
The position of a particle is given by the parametric
equations x = sin(t) and y
represents time. We know that the shape of the path
of the particle is a circle.
cos(t) where t
a) How long does it take the particle to go once
around the circle? Find parametric equations if the
particle moves twice as fast around the circle.
b) Does the particle travel clockwise or
counterclockwise around the circle? Find parametric
equations if the particle moves in the opposite
direction around the circle.
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