Simple Harmonic Motion and frequency of a spring

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Homework Help Overview

The discussion revolves around a problem involving simple harmonic motion (SHM) and the quality factor (Q) of a spring-mass system. The original poster presents a scenario where a 2 kg mass is attached to a spring, which extends by 2.5 cm, and the system oscillates with a small amplitude. The inquiry focuses on understanding the concept of Q and its implications for angular frequency.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to clarify the definition of Q in the context of the system. Questions are raised about the nature of SHM in this scenario, particularly regarding the influence of gravity. Some participants suggest that Q relates to the frequency and damping characteristics of the system.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of Q and its relevance to the system's behavior. Some guidance has been offered regarding the relationship between Q, damping, and angular frequency, but there is no consensus on the next steps or a complete understanding of the problem.

Contextual Notes

Participants note that the spring is assumed to have negligible mass, and the problem setup involves specific parameters such as the mass, spring extension, and amplitude of oscillation. There is an emphasis on the need for further clarification regarding the definitions and implications of Q in this context.

kidia
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I have one question here,I fail to understood what is Q of the system,is anybody has an ideal on this?

An object of mass 2 kg hangs from spring of negligible mass. The spring is extended by 2.5 cm when the object is attached. The top end of the spring is oscillated up and down in SHM with amplitude of 1 mm. The Q of the system is 15.

What is angular frequency for this system?
 
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kidia said:
I have one question here,I fail to understood what is Q of the system,is anybody has an ideal on this?

"Q" is just a symbol until it is given a definition. What does your book say about it? What do your class notes say about it?

An object of mass 2 kg hangs from spring of negligible mass. The spring is extended by 2.5 cm when the object is attached. The top end of the spring is oscillated up and down in SHM with amplitude of 1 mm. The Q of the system is 15.

The system will certainly not execute SHM. It is driven by gravity.

What is angular frequency for this system?

What have you tried so far?
 
Sounds like Q is the frequency.
 
kidia said:
I have one question here,I fail to understood what is Q of the system,is anybody has an ideal on this?

An object of mass 2 kg hangs from spring of negligible mass. The spring is extended by 2.5 cm when the object is attached. The top end of the spring is oscillated up and down in SHM with amplitude of 1 mm. The Q of the system is 15.

What is angular frequency for this system?

Q is the quality factor. it is an indirect measure of the damping. A large Q means that the damping is small, the oscillation takes a while to die off (assuming no external force of course).

If I recall, [itex]Q = { \omega_d \over (b/m) }= {m \omega_d \over b}[/itex]

where [itex]\omega_d \approx \omega_0[/itex].
From the fact that spring extends 2.5 cm with a mass of 2 kg you can find the spring constant. So you know omega_0. Knowing Q then gives you a way to find the damping constant. I am not sure about the rest of the steps, though...

Pat
 

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