Finding the spring constant of a mass in SHM

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Homework Help Overview

The discussion revolves around a problem involving simple harmonic motion (SHM) and the calculation of the spring constant for a mass attached to a spring. The original poster presents a scenario where a 1 g mass is oscillating, with specific initial conditions provided for displacement and acceleration.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply the formula ma = -kx but encounters discrepancies in their results. Participants question whether all forces acting on the mass, including gravity, have been considered. There is a discussion about the applicability of SHM principles in vertical motion compared to horizontal motion.

Discussion Status

The conversation is ongoing, with participants providing guidance on considering all relevant forces and checking the consistency of the initial conditions. There is no explicit consensus on the correct approach or answer yet, as participants are exploring different interpretations of the problem.

Contextual Notes

Participants note the importance of ensuring that all forces, including gravitational force, are accounted for in the calculations. There is also mention of potential transcription errors in the initial conditions provided by the original poster.

KiNGGeexD
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Question:

This is question from A.P French vibrations and waves, problem 3-1 for anyone whom may have it

An object of mass 1 g is hung from a spring and set in oscillatory motion. At t=0 the displacement is 43.785 cm and the acceleration is -1.7514 cm/sec^2. What is the spring constant?

My attempt:

I thought this problem straight forward and used

ma= -kx

using the numbers above but it gave the wrong answer? And I changed everything into S.I units I should also say

The answer is 0.025 N/m or 25 dyn/cm

I have been messing around with this for a while and gotten no where close to the correct answer! Rather frustrating considering it is such a straight forward problem Any help would be great thanks in advanced
 
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Have you considered ALL the forces working on the object? Make sure For something to hang from a spring, what force is required?
 
Gravity would be required! But is it not true that simple harmonic motion obeys the same laws in the vertical direction as it does in the horizontal?
 
The laws of motion (simple harmonic and otherwise) must consider ALL the forces.
 
Would I just then have

ma- mg= -kx
 
I think you have included all the relevant forces. What answer do you get? Does it agree with the given answer? If not, is the given answer rounded? Are the initial conditions you posted the actual ones given in the problem (transcription errors are common)?

Finally, it never hurts to check that all your displacements, accelerations and forces are consistent with your choice of coordinate system.

Sorry I can't be more explicit. I have been admonished in the past for being too helpful.
 
My answer came out to be

26 dyn/cm
 

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