All Questions
10
questions
1
vote
1
answer
130
views
Why can we ignore the work done by gravity?
I am working through the problem above, starting with part (d). By the conservation of energy setting the spring in equilibrium as $y_0$ as the difference in length of the unstretched spring to the ...
0
votes
1
answer
85
views
Schrödinger-Propagator for combined linear and harmonic potential
Given the Hamiltonian
\begin{equation}
H = \frac{p^2}{2m} + V(x)
\end{equation}
The propagator for a pure harmonic potential of the form
\begin{equation}
V(x) = \frac{1}{2} m \omega^2 x^2
\end{...
- 141
0
votes
1
answer
330
views
Doubt from Arnold; Mathematical methods of classical mechanics (page 20)
I am trying to do a problem from Arnold; Mathematical methods of Classical mechanics.
But I didn't get the desired result mentioned by the author.
Let $E_0$ be the value of the potential function at ...
- 23
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
-3
votes
1
answer
67
views
Frequency of vibration from potential field [closed]
I have an equation:
$$V = 200x^2 + 150 ergs/gm$$
How can I get the frequency of its vibration? (I have the mass of object which is 4gm)
I don't know where to start to solve this. Please help.
- 127
-3
votes
1
answer
612
views
Oscillation of a simple pendulum [closed]
What is maximum possible time period of oscillation of a simple pendulum on earth? Please elaborate your answers.
4
votes
1
answer
442
views
Period on the phase plane (small oscillations)
I have this formula to calculate the period of a motion in the phase space (plan, in this case) along a phase curve.
\begin{equation}
T(E)=\int_{x_1}^{x_2}\frac{dx}{\sqrt{2(E-U(x))}}
\end{equation}
...
- 1,704
1
vote
1
answer
334
views
Why does $\omega = \sqrt{V''(x_0) / m}$?
I know that in an equation such that $$\ddot{x} + \omega^2x = 0,$$ the angular frequency $ = \omega$. But why is that ever $ \sqrt{V''(x_0) / m}$? (where $x_0$ is the equilibrium point). I just saw ...
- 171
0
votes
2
answers
765
views
Simple harmonic oscillator, calculate the trajectory in real space
Potential of a simple harmonic oscillator:
$$U=\frac{1}{2}k x^2$$
I'm asked to calculate the trajectory of a particle moving in this potential, with initial conditions $x(t=0) = 0$ and $v(t=0)=v_0$.
...
- 11
1
vote
2
answers
644
views
Potential energy during vertical fall
Suppose I have a weightless spring connected perpendicularly to the ground, and it has on top of it some weightless surface. Now, I release some sticky object from height $h$ above the system of light ...
- 169