Consider the following position functions r and R for two objects. a. Find the interval [c, d] over which the R trajectory is the same as the r trajectory over [a,b]. b. Find the velocity of both objects. c. Graph the speed of the two objects over the intervals [a,b] and [c,d], respectively. r(t) = (cost,3 sin t), [a,b] = [0,2π] R(t) = (cos 5t,3 sin 5t) on [c, d] a. The interval is
Consider the following position functions r and R for two objects. a. Find the interval [c, d] over which the R trajectory is the same as the r trajectory over [a,b]. b. Find the velocity of both objects. c. Graph the speed of the two objects over the intervals [a,b] and [c,d], respectively. r(t) = (cost,3 sin t), [a,b] = [0,2π] R(t) = (cos 5t,3 sin 5t) on [c, d] a. The interval is
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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![**Transcription for Educational Website:**
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Consider the following position functions **r** and **R** for two objects.
a. Find the interval \([c, d]\) over which the **R** trajectory is the same as the **r** trajectory over \([a, b]\).
b. Find the velocity of both objects.
c. Graph the speed of the two objects over the intervals \([a, b]\) and \([c, d]\), respectively.
\[
\mathbf{r}(t) = \langle \cos t, 3 \sin t \rangle , \; [a, b] = [0, 2\pi]
\]
\[
\mathbf{R}(t) = \langle \cos 5t, 3 \sin 5t \rangle \; \text{on} \; [c, d]
\]
---
**Solution:**
a. The interval is \([ \, \, ]\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ade5d6c-ff37-4df2-b1de-522b52697cc9%2F332b6b80-3abe-446c-babe-91c2e52aa34d%2Fnoergjf_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website:**
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Consider the following position functions **r** and **R** for two objects.
a. Find the interval \([c, d]\) over which the **R** trajectory is the same as the **r** trajectory over \([a, b]\).
b. Find the velocity of both objects.
c. Graph the speed of the two objects over the intervals \([a, b]\) and \([c, d]\), respectively.
\[
\mathbf{r}(t) = \langle \cos t, 3 \sin t \rangle , \; [a, b] = [0, 2\pi]
\]
\[
\mathbf{R}(t) = \langle \cos 5t, 3 \sin 5t \rangle \; \text{on} \; [c, d]
\]
---
**Solution:**
a. The interval is \([ \, \, ]\).
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