Oscillation of a vertical spring

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Homework Help Overview

The discussion revolves around the oscillation of a mass attached to a vertical spring, specifically analyzing the frequency of small oscillations and the effects of an external driving force on the spring's length. The problem involves concepts from mechanics and harmonic motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the equations of motion for the mass and the spring, questioning the validity of assumptions regarding forces acting on the spring's ends. They discuss the relationship between the mass's acceleration and the spring's length, and the implications of external forces on the system.

Discussion Status

There is ongoing exploration of the correct formulation of the equations governing the system. Some participants have provided guidance on how to denote the positions of the spring's ends and the mass, while others are questioning the assumptions made about forces and accelerations. Multiple interpretations of the problem are being considered, particularly regarding the effects of the external driving force.

Contextual Notes

Participants are navigating the constraints of the problem, including the assumption of negligible mass for the spring and the need for clarity on the initial conditions for the oscillation. There is also a focus on ensuring that the terms used in the equations accurately reflect the physical setup described in the problem statement.

  • #61
See the figure: It shows the time dependence of both the length L and the position of the mass, (y) for the case when w=2pi, n=4pi, c=0.1 b=1.Note how much less the mass moves compared to the spring.

Also watch the video about an experiment with a slinky. The top of the slinky is released and falls down, while the mass at the bottom stays almost motionless except the last stage when the slinky gets relaxed.

http://www.youtube.com/watch?v=oKb2tCtpvNU&NR=1

ehild
 

Attachments

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