ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 29 Oct 2013 10:28:34 +0100physics problem solving with differential equationshttps://ask.sagemath.org/question/9811/physics-problem-solving-with-differential-equations/Hi,
I'm new in this community.
I want to solve a physic problem which requires differential equation system solutions.
I don't know if my equations are correctly set. Any suggestion is good.
My problem is described by this image: http://img805.imageshack.us/img805/7043/lllzm.png
I have two masses (1/3*m the first, 2/3*m the second) linked with a rope. The rope is free to slide around a nail (the big black point in the image). The image shows the starting condition: a man keeps the first mass stopped and so the rope is kept stretched by the second mass.
I search three functions describing the kinematics of two masses after the man will leave the fist mass: vertical movement of mass A y(t), vertical movement of mass B j(t), and horizontal movement of mass B x(t).
My Cartesian reference system is x-y system in the image.
I have to solve the following equations:
1) -2/3*m*g+T=2/3*m*d2/dt2_y
2) -1/3m*g+Sy=1/3*m*d2/dt2_j
3) Sx=1/3*m*d2/dt2_x
4) abs(T)=sqrt(Sx^2+Sy^2)
5) abs(y(t))=sqrt(x(t)^2+j(t)^2)
From the forth and the fifth equations I obtain two equations, so I have 5 equations in 5 unknowns. They are:
1) T force sustaining the second mass
2) Sx x-component of force sustaining the first mass
3) Sy y-component of force sustaining the first mass
4) y(t) position of the second mass
5) x(t) x-position of the first mass
6) j(t) y-position of the first mass
I hope my explanation is clear.
How can I obtain my solutions using Sage?
Thank you very much!!
Sat, 16 Feb 2013 14:17:39 +0100https://ask.sagemath.org/question/9811/physics-problem-solving-with-differential-equations/Answer by sps for <p>Hi,
I'm new in this community.</p>
<p>I want to solve a physic problem which requires differential equation system solutions.</p>
<p>I don't know if my equations are correctly set. Any suggestion is good.
My problem is described by this image: <a href="http://img805.imageshack.us/img805/7043/lllzm.png">http://img805.imageshack.us/img805/70...</a></p>
<p>I have two masses (1/3<em>m the first, 2/3</em>m the second) linked with a rope. The rope is free to slide around a nail (the big black point in the image). The image shows the starting condition: a man keeps the first mass stopped and so the rope is kept stretched by the second mass.</p>
<p>I search three functions describing the kinematics of two masses after the man will leave the fist mass: vertical movement of mass A y(t), vertical movement of mass B j(t), and horizontal movement of mass B x(t).</p>
<p>My Cartesian reference system is x-y system in the image. </p>
<p>I have to solve the following equations:
1) -2/3<em>m</em>g+T=2/3<em>m</em>d2/dt2_y
2) -1/3m<em>g+Sy=1/3</em>m<em>d2/dt2_j
3) Sx=1/3</em>m*d2/dt2_x
4) abs(T)=sqrt(Sx^2+Sy^2)
5) abs(y(t))=sqrt(x(t)^2+j(t)^2)</p>
<p>From the forth and the fifth equations I obtain two equations, so I have 5 equations in 5 unknowns. They are:
1) T force sustaining the second mass
2) Sx x-component of force sustaining the first mass
3) Sy y-component of force sustaining the first mass
4) y(t) position of the second mass
5) x(t) x-position of the first mass
6) j(t) y-position of the first mass</p>
<p>I hope my explanation is clear.</p>
<p>How can I obtain my solutions using Sage?</p>
<p>Thank you very much!!</p>
https://ask.sagemath.org/question/9811/physics-problem-solving-with-differential-equations/?answer=14553#post-id-14553I want to solve a physic problem which requires differential equation system solutions.
I don't know if my equations are correctly set. Any suggestion is good. My problem is described by this image: http://img805.imageshack.us/img805/7043/lllzm.png
I have two masses (1/3m the first, 2/3m the second) linked with a rope. The rope is free to slide around a nail (the big black point in the image). The image shows the starting condition: a man keeps the first mass stopped and so the rope is kept stretched by the second mass.
I search three functions describing the kinematics of two masses after the man will leave the fist mass: vertical movement of mass A y(t), vertical movement of mass B j(t), and horizontal movement of mass B x(t).
My Cartesian reference system is x-y system in the image.
I have to solve the following equations: 1)
1. List item -2/3mg+T=2/3md2/dt2_y
2. List item -1/3mg+Sy=1/3md2/dt2_j
3. List item Sx=1/3m*d2/dt2_x
4. List item abs(T)=sqrt(Sx^2+Sy^2)
5. List item abs(y(t))=sqrt(x(t)^2+j(t)^2)
From the forth and the fifth equations I obtain two equations, so I have 5 equations in 5 unknowns. They are:
1. List item T force sustaining the second mass
2. List item Sx x-component of force sustaining the first mass
3. List item Sy y-component of force sustaining the first mass
4. List item y(t) position of the second mass
5. List item x(t) x-position of the first mass
6. List item j(t) y-position of the first mass
I hope my explanation is clear.
How can I obtain my solutions using Sage?
Thank you very much!!Sat, 16 Feb 2013 14:22:26 +0100https://ask.sagemath.org/question/9811/physics-problem-solving-with-differential-equations/?answer=14553#post-id-14553Comment by psp for <p>I want to solve a physic problem which requires differential equation system solutions.</p>
<p>I don't know if my equations are correctly set. Any suggestion is good. My problem is described by this image: <a href="http://img805.imageshack.us/img805/7043/lllzm.png">http://img805.imageshack.us/img805/70...</a></p>
<p>I have two masses (1/3m the first, 2/3m the second) linked with a rope. The rope is free to slide around a nail (the big black point in the image). The image shows the starting condition: a man keeps the first mass stopped and so the rope is kept stretched by the second mass.</p>
<p>I search three functions describing the kinematics of two masses after the man will leave the fist mass: vertical movement of mass A y(t), vertical movement of mass B j(t), and horizontal movement of mass B x(t).</p>
<p>My Cartesian reference system is x-y system in the image.</p>
<p>I have to solve the following equations: 1) </p>
<ol>
<li>List item -2/3mg+T=2/3md2/dt2_y </li>
<li>List item -1/3mg+Sy=1/3md2/dt2_j </li>
<li>List item Sx=1/3m*d2/dt2_x </li>
<li>List item abs(T)=sqrt(Sx^2+Sy^2) </li>
<li>List item abs(y(t))=sqrt(x(t)^2+j(t)^2)</li>
</ol>
<p>From the forth and the fifth equations I obtain two equations, so I have 5 equations in 5 unknowns. They are:
1. List item T force sustaining the second mass
2. List item Sx x-component of force sustaining the first mass
3. List item Sy y-component of force sustaining the first mass
4. List item y(t) position of the second mass
5. List item x(t) x-position of the first mass
6. List item j(t) y-position of the first mass</p>
<p>I hope my explanation is clear.</p>
<p>How can I obtain my solutions using Sage?</p>
<p>Thank you very much!!</p>
https://ask.sagemath.org/question/9811/physics-problem-solving-with-differential-equations/?comment=16834#post-id-16834No one could help me anyway? Just suggestions? Nothing?Tue, 29 Oct 2013 10:28:34 +0100https://ask.sagemath.org/question/9811/physics-problem-solving-with-differential-equations/?comment=16834#post-id-16834Comment by psp for <p>I want to solve a physic problem which requires differential equation system solutions.</p>
<p>I don't know if my equations are correctly set. Any suggestion is good. My problem is described by this image: <a href="http://img805.imageshack.us/img805/7043/lllzm.png">http://img805.imageshack.us/img805/70...</a></p>
<p>I have two masses (1/3m the first, 2/3m the second) linked with a rope. The rope is free to slide around a nail (the big black point in the image). The image shows the starting condition: a man keeps the first mass stopped and so the rope is kept stretched by the second mass.</p>
<p>I search three functions describing the kinematics of two masses after the man will leave the fist mass: vertical movement of mass A y(t), vertical movement of mass B j(t), and horizontal movement of mass B x(t).</p>
<p>My Cartesian reference system is x-y system in the image.</p>
<p>I have to solve the following equations: 1) </p>
<ol>
<li>List item -2/3mg+T=2/3md2/dt2_y </li>
<li>List item -1/3mg+Sy=1/3md2/dt2_j </li>
<li>List item Sx=1/3m*d2/dt2_x </li>
<li>List item abs(T)=sqrt(Sx^2+Sy^2) </li>
<li>List item abs(y(t))=sqrt(x(t)^2+j(t)^2)</li>
</ol>
<p>From the forth and the fifth equations I obtain two equations, so I have 5 equations in 5 unknowns. They are:
1. List item T force sustaining the second mass
2. List item Sx x-component of force sustaining the first mass
3. List item Sy y-component of force sustaining the first mass
4. List item y(t) position of the second mass
5. List item x(t) x-position of the first mass
6. List item j(t) y-position of the first mass</p>
<p>I hope my explanation is clear.</p>
<p>How can I obtain my solutions using Sage?</p>
<p>Thank you very much!!</p>
https://ask.sagemath.org/question/9811/physics-problem-solving-with-differential-equations/?comment=16866#post-id-16866no one could help me? Is it to difficult this problem?Thu, 24 Oct 2013 13:30:59 +0200https://ask.sagemath.org/question/9811/physics-problem-solving-with-differential-equations/?comment=16866#post-id-16866