amplitude-length of sine curve
$begingroup$
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 SkartadouGeorgia Skartadou
112
$endgroup$
add a comment |
$begingroup$
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 SkartadouGeorgia Skartadou
112
$endgroup$
add a comment |
$begingroup$
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 SkartadouGeorgia Skartadou
112
$endgroup$
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 SkartadouGeorgia Skartadou
112
edited Apr 13 '17 at 12:20
Community♦
1
asked May 31 '15 at 15:17
Georgia SkartadouGeorgia Skartadou
112
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 SkartadouGeorgia Skartadou
112
asked May 31 '15 at 15:17
Georgia SkartadouGeorgia Skartadou
112
asked May 31 '15 at 15:17
Georgia SkartadouGeorgia Skartadou
112
112
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
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 NovatiEmilio Novati
51.9k43474
$endgroup$
$begingroup$
thanks for the quick answer!This seems to be altering the sine function,though..It doesn't result in a symmetrical distribution of values
$endgroup$
– Georgia Skartadou
May 31 '15 at 15:40
$begingroup$
I have added an amplitude for the oscillations, but I don't understand what you mean for ''symmetrical distribution''.
$endgroup$
– Emilio Novati
May 31 '15 at 15:50
$begingroup$
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
$endgroup$
– Georgia Skartadou
May 31 '15 at 16:55
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1306597%2famplitude-length-of-sine-curve%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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 NovatiEmilio Novati
51.9k43474
$endgroup$
$begingroup$
thanks for the quick answer!This seems to be altering the sine function,though..It doesn't result in a symmetrical distribution of values
$endgroup$
– Georgia Skartadou
May 31 '15 at 15:40
$begingroup$
I have added an amplitude for the oscillations, but I don't understand what you mean for ''symmetrical distribution''.
$endgroup$
– Emilio Novati
May 31 '15 at 15:50
$begingroup$
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
$endgroup$
– Georgia Skartadou
May 31 '15 at 16:55
add a comment |
$begingroup$
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 NovatiEmilio Novati
51.9k43474
$endgroup$
$begingroup$
thanks for the quick answer!This seems to be altering the sine function,though..It doesn't result in a symmetrical distribution of values
$endgroup$
– Georgia Skartadou
May 31 '15 at 15:40
$begingroup$
I have added an amplitude for the oscillations, but I don't understand what you mean for ''symmetrical distribution''.
$endgroup$
– Emilio Novati
May 31 '15 at 15:50
$begingroup$
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
$endgroup$
– Georgia Skartadou
May 31 '15 at 16:55
add a comment |
$begingroup$
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 NovatiEmilio Novati
51.9k43474
$endgroup$
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 NovatiEmilio Novati
51.9k43474
edited May 31 '15 at 15:50
answered May 31 '15 at 15:36
Emilio NovatiEmilio Novati
51.9k43474
answered May 31 '15 at 15:36
Emilio NovatiEmilio Novati
51.9k43474
answered May 31 '15 at 15:36
Emilio NovatiEmilio Novati
51.9k43474
51.9k43474
$begingroup$
thanks for the quick answer!This seems to be altering the sine function,though..It doesn't result in a symmetrical distribution of values
$endgroup$
– Georgia Skartadou
May 31 '15 at 15:40
$begingroup$
I have added an amplitude for the oscillations, but I don't understand what you mean for ''symmetrical distribution''.
$endgroup$
– Emilio Novati
May 31 '15 at 15:50
$begingroup$
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
$endgroup$
– Georgia Skartadou
May 31 '15 at 16:55
add a comment |
$begingroup$
thanks for the quick answer!This seems to be altering the sine function,though..It doesn't result in a symmetrical distribution of values
$endgroup$
– Georgia Skartadou
May 31 '15 at 15:40
$begingroup$
I have added an amplitude for the oscillations, but I don't understand what you mean for ''symmetrical distribution''.
$endgroup$
– Emilio Novati
May 31 '15 at 15:50
$begingroup$
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
$endgroup$
– Georgia Skartadou
May 31 '15 at 16:55
$begingroup$
thanks for the quick answer!This seems to be altering the sine function,though..It doesn't result in a symmetrical distribution of values
$endgroup$
– Georgia Skartadou
May 31 '15 at 15:40
$begingroup$
thanks for the quick answer!This seems to be altering the sine function,though..It doesn't result in a symmetrical distribution of values
$endgroup$
– Georgia Skartadou
May 31 '15 at 15:40
$begingroup$
I have added an amplitude for the oscillations, but I don't understand what you mean for ''symmetrical distribution''.
$endgroup$
– Emilio Novati
May 31 '15 at 15:50
$begingroup$
I have added an amplitude for the oscillations, but I don't understand what you mean for ''symmetrical distribution''.
$endgroup$
– Emilio Novati
May 31 '15 at 15:50
$begingroup$
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
$endgroup$
– Georgia Skartadou
May 31 '15 at 16:55
$begingroup$
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
$endgroup$
– Georgia Skartadou
May 31 '15 at 16:55
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1306597%2famplitude-length-of-sine-curve%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
