Simple Harmonic Motion and displacement

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Homework Help Overview

The discussion revolves around a problem involving simple harmonic motion and the relationship between mass, spring constant, and displacement in a spring system. The original poster presents a scenario where a block is hung from a spring, and a second block is added, resulting in increased displacement.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply the formula for spring force and gravitational force, expressing their calculations in terms of mass and displacement. Some participants suggest maintaining symbolic representations instead of substituting numerical values. Others explore the relationship between the total mass and the displacement caused by the spring.

Discussion Status

The discussion is ongoing, with participants providing guidance on how to approach the problem symbolically. There is an exploration of the relationships between the masses and the resulting forces, but no consensus has been reached on the correct solution yet.

Contextual Notes

Participants are navigating algebraic expressions and the implications of using specific values for the spring constant. There is a focus on ensuring clarity in the representation of the problem without substituting arbitrary numbers.

IAmSparticus
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1. A 0.69 kg block is hung from and stretches a spring that is attached to the ceiling. A second block is attached to the first one, and the amount that the spring stretches from its unstrained length increases by a factor of 5. What is the mass of the second block?



2. Force= spring constant*displacement of spring from unstrained length



3. First off, I'm horrible at algebra so sorry if I make stupid mistakes in this attempt. The force is gravity so that becomes mg (.69kg*9.8 m/s/s).

mg=kx

If I pick a spring constant of 10 (does it matter what I pick?) then the equation becomes:

(.69kg)(9.8m/s/s)=10 x

Which would give a displacement of .6762 m. Now, when we increase it by a factor of 5, that displacement becomes 3.381 m. Plugging that into a new equations gives:

m (9.8m/s/s) = 10 (3.381m)

When I solve for m I get 3.45 kg, which is wrong. Someone tell me what I did wrong?
 
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m is the total mass of the first and second blocks. Try to leave your work in symbols rather than substitute arbitrary numbers; its neater that way.
 
So if I leave it in the symbol format I get that (.69kg)(9.8m/s/s)=kx and m(9.8m/s/s)=k(5x). Now what?
 
(m1 + m2)g = 5 (kx) = 5 (m1)g
:. m2 = 4 m1
 

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