All Questions
22
questions
1
vote
1
answer
320
views
Obtaining Euler-Lagrange equations for a mass attached to a spring, connected to a pendulum via a pulley [closed]
I'm trying to setup the Lagrangian for the following system, I'm quite confident this is correct, but I would like a second pair of eyes to analyse my solution. Here is the problem at hand
A block ...
- 131
0
votes
2
answers
339
views
Constraint equation for an elastic pendulum
I would like to know if you can help me determine the restraining force for an elastic pendulum. The problem is the following
A particle of mass $m$ is suspended by a massless spring of length $L$. ...
- 125
1
vote
2
answers
206
views
Lagrangian function for two swivelling masses attached by a spring
I am just having a hard time finding the Lagrangian for this question. There are two massless rigid rods lengths R (connected to mass M) and r (connected to mass m) which both pivot around a fixed ...
- 29
0
votes
1
answer
68
views
Potential Energy of 'Triple Spring Mass System'
Given the following system, I am trying to find the potential energy and equations of motion.
$\hspace{70mm}$
What I got is
$$\Pi = \frac{1}{2}(c_1(\varphi_2r_2-\varphi_1r_1)^2 + c_2(\varphi_2r_2-\...
- 3
0
votes
2
answers
462
views
Lagrangian of an elastic pendulum
I'm trying to understand the way my teacher found the Lagrangian of an elastic pendulum.
Given a spring pendulum connected to the origin, the equilibrium point is $(0,0,\frac{-mg}{k})$.
The length of ...
- 449
0
votes
0
answers
325
views
Lagrangian for spring mass pulley systems
Recently I came across a question relating to a spring mass system with pulleys. So I decided to try and write its Lagrangian. However I have run into a problem. The expression for a spring's ...
- 1,850
0
votes
1
answer
106
views
Anharmonic terms of Lagrangian of spring pendulum with free support
I am trying to find the normal modes of a spring pendulum with moving support. The spring has spring constant $k$ and unstretched length $l_0$.
Sorry for my bad paint skills. The problem was stated ...
- 324
0
votes
0
answers
228
views
Mechanics of an (infinite small) spring oscillator
I've been thinking about creating a continuous rope, made out of infinitely many springs, with infinitely small distances between them.
At first, I developed the Euler-Lagrange Equations:
$$
\mathcal{...
- 1,525
1
vote
1
answer
339
views
Validity of using Lagrange equations in an elastic pendulum
To derive Lagrange equation of motion, which are
$$\frac d {dt} \frac {\partial L} {\partial \dot q}-\frac {\partial L} {\partial q} =0$$
we need the virtual work of constraint to be zero , as is said ...
- 1,270
1
vote
1
answer
225
views
Particles connected with spring, sliding over lines. Question about the potential energy
I'm currently studying small oscillations with the Lagrangian formalism. I stumbled upon an exercise that I can't seem to understand the method of solving it.
Two particles $P_1$ and $P_2$, with the ...
- 77
0
votes
1
answer
161
views
Lagrangian with compound elastic pendulum
Please refer to the attached image (please excuse my poor drawings skills).
Excuse my language etiquette as I am an engineer, and may not be familiar with all the correct terminology.
The system ...
- 1
0
votes
1
answer
259
views
Meaning of Lagrange multiplier for a particle in a cylinder with a spring
My procedure is the following in cylindrical coordinates ($\rho,\theta,z$):
The kinetic energy,
\begin{equation}
T=\frac{1}{2} m v^{2}=\frac{1}{2} m\left(\dot{p}^{2}+\rho^{2} \theta^{2}+\dot{z}^{2}\...
- 7
0
votes
1
answer
660
views
Trouble finding the matrix form of potential energy in small oscillations (Goldstein linear triatomic molecule example)
I'm currently trying to learn small oscillations, I kind of comprehend the general theory, but I'm having hard times finding the matrix forms of the potential and kinetic energy. I have been following ...
- 7
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