amplitude-length of sine curve
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I have an equation of the following form:
$y=Acdot sin(Fcdot x)$
I want to create a sine function on a circle,somehow like the image:
I want it to include 6 repeats of the function therefore if the length of the circle is computed as:
length=$2cdot picdot R$ ($R$=radius)
the period will be length/6:
Period=$2cdot picdot frac{R}{6}$
and F will be:
$F=2cdot frac{pi}{Period}$
Now I was wandering how can I keep the total length of the sine curve,as well as the number of repeats (meaning the period-F) stable and change the amplitude in order to have a curve that remains of stable length while the radius of circle increases-decreases.
In order to manage this I have ended up at the intergral describing the length of a sine curve, meaning the type described in this post:
What is the length of a sine wave from $0$ to $2pi$?$0$-to-$2-pi$
I want to end up in a formula describing the amplitude in terms of length, so I want some help in understanding how do we compute the integral of a sine curve length..
Ideas, and any kind of help are welcome!
Thanking everyone in advance
trigonometry
edited Apr 13 '17 at 12:20
Community♦
1
asked May 31 '15 at 15:17
Georgia Skartadou
111
add a comment |
up vote
2
down vote
favorite
I have an equation of the following form:
$y=Acdot sin(Fcdot x)$
I want to create a sine function on a circle,somehow like the image:
I want it to include 6 repeats of the function therefore if the length of the circle is computed as:
length=$2cdot picdot R$ ($R$=radius)
the period will be length/6:
Period=$2cdot picdot frac{R}{6}$
and F will be:
$F=2cdot frac{pi}{Period}$
Now I was wandering how can I keep the total length of the sine curve,as well as the number of repeats (meaning the period-F) stable and change the amplitude in order to have a curve that remains of stable length while the radius of circle increases-decreases.
In order to manage this I have ended up at the intergral describing the length of a sine curve, meaning the type described in this post:
What is the length of a sine wave from $0$ to $2pi$?$0$-to-$2-pi$
I want to end up in a formula describing the amplitude in terms of length, so I want some help in understanding how do we compute the integral of a sine curve length..
Ideas, and any kind of help are welcome!
Thanking everyone in advance
trigonometry
edited Apr 13 '17 at 12:20
Community♦
1
asked May 31 '15 at 15:17
Georgia Skartadou
111
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
I have an equation of the following form:
$y=Acdot sin(Fcdot x)$
I want to create a sine function on a circle,somehow like the image:
I want it to include 6 repeats of the function therefore if the length of the circle is computed as:
length=$2cdot picdot R$ ($R$=radius)
the period will be length/6:
Period=$2cdot picdot frac{R}{6}$
and F will be:
$F=2cdot frac{pi}{Period}$
Now I was wandering how can I keep the total length of the sine curve,as well as the number of repeats (meaning the period-F) stable and change the amplitude in order to have a curve that remains of stable length while the radius of circle increases-decreases.
In order to manage this I have ended up at the intergral describing the length of a sine curve, meaning the type described in this post:
What is the length of a sine wave from $0$ to $2pi$?$0$-to-$2-pi$
I want to end up in a formula describing the amplitude in terms of length, so I want some help in understanding how do we compute the integral of a sine curve length..
Ideas, and any kind of help are welcome!
Thanking everyone in advance
trigonometry
edited Apr 13 '17 at 12:20
Community♦
1
asked May 31 '15 at 15:17
Georgia Skartadou
111
I have an equation of the following form:
$y=Acdot sin(Fcdot x)$
I want to create a sine function on a circle,somehow like the image:
I want it to include 6 repeats of the function therefore if the length of the circle is computed as:
length=$2cdot picdot R$ ($R$=radius)
the period will be length/6:
Period=$2cdot picdot frac{R}{6}$
and F will be:
$F=2cdot frac{pi}{Period}$
Now I was wandering how can I keep the total length of the sine curve,as well as the number of repeats (meaning the period-F) stable and change the amplitude in order to have a curve that remains of stable length while the radius of circle increases-decreases.
In order to manage this I have ended up at the intergral describing the length of a sine curve, meaning the type described in this post:
What is the length of a sine wave from $0$ to $2pi$?$0$-to-$2-pi$
I want to end up in a formula describing the amplitude in terms of length, so I want some help in understanding how do we compute the integral of a sine curve length..
Ideas, and any kind of help are welcome!
Thanking everyone in advance
trigonometry
trigonometry
edited Apr 13 '17 at 12:20
Community♦
1
asked May 31 '15 at 15:17
Georgia Skartadou
111
edited Apr 13 '17 at 12:20
Community♦
1
asked May 31 '15 at 15:17
Georgia Skartadou
111
edited Apr 13 '17 at 12:20
Community♦
1
edited Apr 13 '17 at 12:20
Community♦
1
edited Apr 13 '17 at 12:20
Community♦
1
1
asked May 31 '15 at 15:17
Georgia Skartadou
111
asked May 31 '15 at 15:17
Georgia Skartadou
111
asked May 31 '15 at 15:17
Georgia Skartadou
111
111
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
up vote
0
down vote
Hint:
You can use an equation in polar coordinates of the form:
$$
r=R+asin(ntheta)
$$
or
$$
r=R+acos(ntheta)
$$
that represent an oscillation around a circle of radius R with $n$ oscillations of amplitude $a$.
See here for an exemple.
answered May 31 '15 at 15:36
Emilio Novati
50.7k43372
thanks for the quick answer!This seems to be altering the sine function,though..It doesn't result in a symmetrical distribution of values
– Georgia Skartadou
May 31 '15 at 15:40
I have added an amplitude for the oscillations, but I don't understand what you mean for ''symmetrical distribution''.
– Emilio Novati
May 31 '15 at 15:50
I mean that it looks as though the distances moved from the central axis(a circle with a radius of 4) are not equal for the points inside the circle and for the points outside of it. I have one more question though: how do polar coordinates ensure that the total length of the sine curve remains unmodified?What I want to achieve can be described as a thread of given length that follows the circular path of a sine curve and when the radius grows up it gets more streched
– Georgia Skartadou
May 31 '15 at 16:55
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Hint:
You can use an equation in polar coordinates of the form:
$$
r=R+asin(ntheta)
$$
or
$$
r=R+acos(ntheta)
$$
that represent an oscillation around a circle of radius R with $n$ oscillations of amplitude $a$.
See here for an exemple.
answered May 31 '15 at 15:36
Emilio Novati
50.7k43372
thanks for the quick answer!This seems to be altering the sine function,though..It doesn't result in a symmetrical distribution of values
– Georgia Skartadou
May 31 '15 at 15:40
I have added an amplitude for the oscillations, but I don't understand what you mean for ''symmetrical distribution''.
– Emilio Novati
May 31 '15 at 15:50
I mean that it looks as though the distances moved from the central axis(a circle with a radius of 4) are not equal for the points inside the circle and for the points outside of it. I have one more question though: how do polar coordinates ensure that the total length of the sine curve remains unmodified?What I want to achieve can be described as a thread of given length that follows the circular path of a sine curve and when the radius grows up it gets more streched
– Georgia Skartadou
May 31 '15 at 16:55
add a comment |
up vote
0
down vote
Hint:
You can use an equation in polar coordinates of the form:
$$
r=R+asin(ntheta)
$$
or
$$
r=R+acos(ntheta)
$$
that represent an oscillation around a circle of radius R with $n$ oscillations of amplitude $a$.
See here for an exemple.
answered May 31 '15 at 15:36
Emilio Novati
50.7k43372
thanks for the quick answer!This seems to be altering the sine function,though..It doesn't result in a symmetrical distribution of values
– Georgia Skartadou
May 31 '15 at 15:40
I have added an amplitude for the oscillations, but I don't understand what you mean for ''symmetrical distribution''.
– Emilio Novati
May 31 '15 at 15:50
I mean that it looks as though the distances moved from the central axis(a circle with a radius of 4) are not equal for the points inside the circle and for the points outside of it. I have one more question though: how do polar coordinates ensure that the total length of the sine curve remains unmodified?What I want to achieve can be described as a thread of given length that follows the circular path of a sine curve and when the radius grows up it gets more streched
– Georgia Skartadou
May 31 '15 at 16:55
add a comment |
up vote
0
down vote
up vote
0
down vote
Hint:
You can use an equation in polar coordinates of the form:
$$
r=R+asin(ntheta)
$$
or
$$
r=R+acos(ntheta)
$$
that represent an oscillation around a circle of radius R with $n$ oscillations of amplitude $a$.
See here for an exemple.
answered May 31 '15 at 15:36
Emilio Novati
50.7k43372
Hint:
You can use an equation in polar coordinates of the form:
$$
r=R+asin(ntheta)
$$
or
$$
r=R+acos(ntheta)
$$
that represent an oscillation around a circle of radius R with $n$ oscillations of amplitude $a$.
See here for an exemple.
answered May 31 '15 at 15:36
Emilio Novati
50.7k43372
edited May 31 '15 at 15:50
answered May 31 '15 at 15:36
Emilio Novati
50.7k43372
answered May 31 '15 at 15:36
Emilio Novati
50.7k43372
answered May 31 '15 at 15:36
Emilio Novati
50.7k43372
50.7k43372
thanks for the quick answer!This seems to be altering the sine function,though..It doesn't result in a symmetrical distribution of values
– Georgia Skartadou
May 31 '15 at 15:40
I have added an amplitude for the oscillations, but I don't understand what you mean for ''symmetrical distribution''.
– Emilio Novati
May 31 '15 at 15:50
I mean that it looks as though the distances moved from the central axis(a circle with a radius of 4) are not equal for the points inside the circle and for the points outside of it. I have one more question though: how do polar coordinates ensure that the total length of the sine curve remains unmodified?What I want to achieve can be described as a thread of given length that follows the circular path of a sine curve and when the radius grows up it gets more streched
– Georgia Skartadou
May 31 '15 at 16:55
add a comment |
thanks for the quick answer!This seems to be altering the sine function,though..It doesn't result in a symmetrical distribution of values
– Georgia Skartadou
May 31 '15 at 15:40
I have added an amplitude for the oscillations, but I don't understand what you mean for ''symmetrical distribution''.
– Emilio Novati
May 31 '15 at 15:50
I mean that it looks as though the distances moved from the central axis(a circle with a radius of 4) are not equal for the points inside the circle and for the points outside of it. I have one more question though: how do polar coordinates ensure that the total length of the sine curve remains unmodified?What I want to achieve can be described as a thread of given length that follows the circular path of a sine curve and when the radius grows up it gets more streched
– Georgia Skartadou
May 31 '15 at 16:55
thanks for the quick answer!This seems to be altering the sine function,though..It doesn't result in a symmetrical distribution of values
– Georgia Skartadou
May 31 '15 at 15:40
thanks for the quick answer!This seems to be altering the sine function,though..It doesn't result in a symmetrical distribution of values
– Georgia Skartadou
May 31 '15 at 15:40
I have added an amplitude for the oscillations, but I don't understand what you mean for ''symmetrical distribution''.
– Emilio Novati
May 31 '15 at 15:50
I have added an amplitude for the oscillations, but I don't understand what you mean for ''symmetrical distribution''.
– Emilio Novati
May 31 '15 at 15:50
I mean that it looks as though the distances moved from the central axis(a circle with a radius of 4) are not equal for the points inside the circle and for the points outside of it. I have one more question though: how do polar coordinates ensure that the total length of the sine curve remains unmodified?What I want to achieve can be described as a thread of given length that follows the circular path of a sine curve and when the radius grows up it gets more streched
– Georgia Skartadou
May 31 '15 at 16:55
I mean that it looks as though the distances moved from the central axis(a circle with a radius of 4) are not equal for the points inside the circle and for the points outside of it. I have one more question though: how do polar coordinates ensure that the total length of the sine curve remains unmodified?What I want to achieve can be described as a thread of given length that follows the circular path of a sine curve and when the radius grows up it gets more streched
– Georgia Skartadou
May 31 '15 at 16:55
add a comment |
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