# Harmonic oscillations We are searching data for your request:

Forums and discussions:
Manuals and reference books:
Data from registers:
Wait the end of the search in all databases.
Upon completion, a link will appear to access the found materials.

## Exercises on harmonic oscillations

### The torsion pendulum

The torsion pendulum in the following figure has a cylinder with the moment of inertia $J=3,2kg⋅m2$ on a steel wire of length $l=5m$ hung up. The benchmark is $D.r=0,81kgm2s-2$. For small twists, there is the dependency for the returning torque $M.$:

$M.=−D.r⋅ϕ$

Initial deflection $ϕ(0)$ of the torsion pendulum is $1wheel$. Let it be assumed that it vibrates without friction.

• Establish the equation of motion for the torsion pendulum and solve the equation of motion.
• How long is the period of the oscillation?
• What are the formulas for potential and kinetic energy?

### Lennard Jones Potential

Goal: Approach of potentials through a harmonic potential for small disturbances / deflections.

The Lennard-Jones potential is made up of a repulsive potential component of the form $B.R.12$, which stems from the Pauli ban, and an attractive potential share of the form $−B.R.6$, which comes from the van der Waals interaction (also London interaction or dipole-dipole interaction).

$U(R.)=4ε[(σR.)12−(σR.)6]$

Approach the potential $U(R.)$ with $ε=14⋅10−23J$ and $σ=2,56⋅10-10m$ around the minimum by a harmonic potential (these values ​​correspond to those for liquid helium at $0K$ and $0Pa$).

1. Togar

I accept it with pleasure. An interesting topic, I will take part. Together we can come to the right answer. I'm sure.

2. Tomi

The amusing information

3. Heathcliff

In my opinion, someone has a letter alexia :)

4. Malrajas

I congratulate, your idea is brilliant

5. Roibeard

I believe that you are wrong. Let's discuss this. Email me at PM, we will talk.

6. Nochehuatl

Same urbanization one