Spring and string pendulum (oscillations)

Click For Summary

Homework Help Overview

The discussion revolves around a pendulum system influenced by a spring, exploring the dynamics of oscillations. The original poster presents a problem involving a pendulum of mass m attached to a string of length L, which is pushed by a spring with spring constant k. The problem includes determining the equation of motion for the angle α, finding the angular frequency, and analyzing the system's behavior at specific initial conditions.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • The original poster attempts to derive the equation of motion and expresses confidence in their initial approach, while also seeking clarification on the equilibrium position and angular frequency. Some participants question the interpretation of initial conditions and the role of gravity in the system. Others suggest revisiting the signs in the equations of motion and the implications of the equilibrium position.

Discussion Status

Participants are actively engaging with the problem, offering insights and corrections to each other's reasoning. There is a productive exchange regarding the formulation of the equations of motion and the effects of various forces acting on the pendulum. While some interpretations differ, the discussion is moving towards a clearer understanding of the dynamics involved.

Contextual Notes

There are ongoing discussions about the initial conditions of the pendulum's motion and the assumptions regarding the equilibrium position. Participants note the lack of explicit information about the initial state of motion, which affects their ability to fully resolve the problem.

  • #31
JulienB said:
@haruspex I imagine so since it was a problem at a real exam a couple of years ago. Well I read the problem again and nothing's stated about t=0 until question c) and it is unfortunately for α = 0 then.
Yes, my remark about t=0 was only in relation to part c.
For part b, the only other suggestion I have is that it should say to find αR in terms of m, L, k and x0.
 
Physics news on Phys.org
  • #32
Also, if I assume that α(0) = αR, I think it implies that B = 0.
 
  • #33
haruspex said:
Yes, my remark about t=0 was only in relation to part c.
For part b, the only other suggestion I have is that it should say to find αR in terms of m, L, k and x0.

Yes and that could be easily done with the force equation right? Well, thank you for your help in any case! Was my reasoning in part c) coherent?Julien
 
  • #34
JulienB said:
Yes and that could be easily done with the force equation right? Well, thank you for your help in any case! Was my reasoning in part c) coherent?Julien
In the equation you posted for α'(0) you had a sign wrong, but that must have been a mistake in typing the post since the answer you got is right.
 
  • Like
Likes   Reactions: JulienB

Similar threads

How do I derive an expression for the velocity vector for any α?
  • · Replies 26 ·
Replies
26
Views
2K
Torque calculation for a compound pendulum
  • · Replies 15 ·
Replies
15
Views
2K
Two spring-coupled masses in an electric field (one of the masses is charged)
  • · Replies 1 ·
Replies
1
Views
1K
Circular Motion - Hanging object swinging around
  • · Replies 7 ·
Replies
7
Views
5K
Rotating simple harmonic oscillator
  • · Replies 11 ·
Replies
11
Views
2K
Determination of the velocity of a particle in a hollow cone
  • · Replies 2 ·
Replies
2
Views
2K
Equation of motion of a dampened pendulum
  • · Replies 3 ·
Replies
3
Views
2K
Simulating a Rotary Inverted Pendulum in Python
  • · Replies 15 ·
Replies
15
Views
2K
How to find period of a SHM concerning a cube and spring?
  • · Replies 5 ·
Replies
5
Views
4K
Foucault Pendulum at the North Pole
  • · Replies 9 ·
Replies
9
Views
2K