Simple Harmonic Motion Question.

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Homework Help Overview

The discussion revolves around a problem in simple harmonic motion involving a mass hung from a spring, which elongates by 10.6 cm. The original poster is tasked with finding the period of oscillations when the mass is displaced from equilibrium, but notes a lack of information regarding the mass and spring constant.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to proceed without knowing the mass or spring constant. Participants inquire about the force due to a spring and reference Hooke's Law. There is a discussion about the forces acting on the mass, particularly the role of gravity and the net force when the system is in equilibrium.

Discussion Status

Participants have engaged in a productive dialogue, exploring the relationship between the forces involved and how to derive the mass-to-spring constant ratio. The original poster acknowledges a realization about the relationship between variables, indicating progress in understanding the problem.

Contextual Notes

The original poster notes the absence of specific values for mass and spring constant, which are critical for solving the problem. The discussion also highlights the importance of recognizing equilibrium conditions in the context of oscillatory motion.

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Homework Statement



When a mass is hung from a spring, the spring elongates by 10.6cm. What will the period of the resulting oscillations be if the mass is displaced from equilibrium?

Homework Equations



T=2(pi)[tex]\sqrt{m/k}[/tex]

The Attempt at a Solution



I have no clue what do with this question, if I am not given a mass or spring constant. I tried using Newtons 2nd Law to find k but without knowing the mass I ended up with two unknowns.
 
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well do you know how to find force due to a spring?
 
cupid.callin said:
well do you know how to find force due to a spring?

Are you talking about hooke's law? F=-kx
 
yes!

Now, which force do you think is responsible for the decrease in height of mass (not -kx one)!
 
cupid.callin said:
yes!

Now, which force do you think is responsible for the decrease in height of mass (not -kx one)!

Well the only other force acting on the object is gravity..
 
yes ... now as you will know that at point where net acc. on body will be zero ... Fnet = 0

can you figure out m/k now?
 
cupid.callin said:
yes ... now as you will know that at point where net acc. on body will be zero ... Fnet = 0

can you figure out m/k now?

Fnet=0
Fs-mg=0
kx=mg
x/g=m/k

(0.106/9.81)=m/k

=0.104= m/k

T=2(pi)square(0.104)root
Got the answer!

Thanks! I was approaching the problem right, I just never noticed m/k=x/g... appreciate the help
 
Last edited:

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