All Questions
33
questions
0
votes
1
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56
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Question about Problem $12$ in Chapter $11$ from Kibble & Berkshire's book
I write again the problem for convinience:
A rigid rod of length $2a$ is suspended by two light, inextensible strings of length $l$ joining its ends to supports also a distance $2a$ apart and level ...
0
votes
0
answers
107
views
Finding the Equation of motion for a vertical rotating disc with an added mass
I have been trying to figure out the equation of motion of a rotating disc with an added mass fixed on the surface of the disc at a certain distance $r$ from the disc's centre point.
I have ...
1
vote
2
answers
217
views
Lagrangian function of a mass-spring-system with deflections in 2D [closed]
I’m looking for the lagrangian function of the following problem (as seen in the picture). We have a mass connected to two springs. We can deglect the mass in two dimensions.
My main problems are:
...
- 11
0
votes
0
answers
45
views
Question about condition for oscillation of a physical system in Lagrangian mechanics
I can't answer the following question about a (simple) physical system I have studied using Lagrangian mechanic techniques.
So, we have a straight rigid rod in a horizontal plane, symmetrically fixed ...
- 1
1
vote
2
answers
694
views
Lagrange equation of motions for a particle moving in a surface in the presence of gravity
I have to model the dynamic behaviour of a particle solid in a gravitational field.It is for a control theory course. And my background in dynamics is not the greatest. The particle can move left and ...
1
vote
0
answers
71
views
Verifying the equation of motion, expressions of kinetic energy and potential energy and how to examine whether motion confined to a plane or not [closed]
A particle is moving in space such that it is attracted towards a fixed point and is proportional to the distance from the fixed point. Derive the Lagrangian and Hamiltonian of the system. Examine ...
- 111
3
votes
1
answer
537
views
Doubt in the expression of Lagrangian of a system [duplicate]
There is a problem given in Goldstein's Classical Mechanics Chapter-1 as
20. A particle of mass $\,m\,$ moves in one dimension such that it has the Lagrangian
\begin{equation}
L\boldsymbol{=}\...
- 436
0
votes
1
answer
111
views
Potential Energy of a Lagrangian System Involving a Mass and Spring [closed]
If you were to calculate the potential energy term of the Lagrangian for this system, would there be an mg term included, or would it be unnecessary as the change in potential energy of the mass would ...
- 3
0
votes
0
answers
40
views
Motion near the local maximum of potential energy
Particle is moving along the $x$ axis in the field with potential energy $U(x)$. $U(x) $has local maximum at $x=0$, and the total energy of particle is equal to $E=U(0)$.
I'm supposed to find how the ...
- 101
0
votes
1
answer
148
views
Particle in a cylinder with a spring, sign convention in potential energy (Lagrangian multipliers)
I'm trying to get the force of constraint. The problem I have is when defying the sign of the potential energy using cylindrical coordinates $(\rho,\phi,z)$, what I have is:
$$
V=mgy-\frac{1}{2}k\left(...
- 7
0
votes
1
answer
569
views
Potential energy of a mass bewteen two springs with pendulum hanging [closed]
I need some help with this problem.
A particle of mass $m_1$ hangs from a rod of negligible mass and length $l$, whose support point consists of another particle of mass $m_2$ that moves horizontally ...
- 103
3
votes
1
answer
840
views
Need help creating the Lagrangian for a coupled pendulum [closed]
I know that for 2 separate single pendulums, the kinetic and potential energies are:
$$KE = \frac{1}{2}I(\dot\theta_1^2 + \dot\theta_2^2)$$
$$PE = 2mgl - mgl(\cos\theta_1 + \cos\theta_2)$$
But I don't ...
- 39
0
votes
1
answer
42
views
Change in potential energy after infinitesimal variation in position
The a particle with the potential $V(x^2+y^2)$ undergoes an active transformation where
$x\rightarrow x+y\delta$
$y\rightarrow y-x\delta$
The exercise was to prove that the Lagrangian of the system ...
- 62
0
votes
3
answers
504
views
The Lagrangian for gravitational potential energy in a double pendulum
For a double pendulum what would be the gravitational energy. I am trying to work out the Lagrangian for the double pendulum. I got the kinetic energy but I am struggling on the gravitational ...
- 119
0
votes
1
answer
101
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To consider or not to consider potential energy of a mass attached to a spring in oscillation? [closed]
For the above system I have the following expressions for kinetic and potential energy:
$$
V = \frac{1}{2}\,k\,x^{2}+m\,g\,l\,(1-cos\,\theta)-m\,g\,x\\ T = \frac{1}{2}\,m\,\dot{x}^{2}+\frac{1}{2}\,m\,...
- 3