Calculate the spring constant of oscillating mass on a spring colliding with a wall

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Homework Help Overview

The discussion revolves around calculating the spring constant for a mass-spring system where the mass collides with a wall. The original poster attempts to derive the spring constant using oscillation time and equations of motion, but encounters discrepancies with the expected answer.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore the implications of the mass bouncing off the wall and question the assumptions made regarding the time of collision and the nature of the oscillation.

Discussion Status

There are multiple interpretations of how the collision affects the oscillation, with some participants suggesting that the collision must be perfectly elastic for periodic motion. Others express confusion about the original poster's calculations and the assumptions made regarding the time of contact with the wall.

Contextual Notes

Participants note that the problem lacks specific details about the time of collision and the coefficient of restitution, which complicates the analysis. The original poster's calculations assume negligible contact time during the collision.

  • #31
But a rather curious coincidence:
If I go by my first interpretation:
Aurelius120 said:
My interpretation was that the given diagram was of the relaxed spring (at ##0##) which would be compressed to left ##(-A)## and released. The wall being on the right ##(+A/2)##. That means one oscillation will be $$(-A)\rightarrow 0\rightarrow \frac{+A}{2} \rightarrow (-A)$$
Period of motion =0.2s given in question is time for ##(-A)\rightarrow 0 \rightarrow \frac{+A}{2} \rightarrow (-A)##
Then $$-A\cos (\omega t)=\frac{+A}{2}$$
$$\implies -\sqrt 2 \cos (\omega t)=\frac{+1}{\sqrt 2}$$
$$\implies \cos (\omega t)=\frac{-1}{2} \implies \omega t=\frac{2\pi}{3}$$
According to question time period of oscillation, 2t=0.2s therefore $$2\omega t= 0.2\omega = \frac{4\pi}{3}$$
This is the same incorrect answer I obtained in POST(1,11,22) and therefore this method is equivalent to that.

Period of motion =0.2s given in question is time for##(-A)\rightarrow 0 \rightarrow \frac{+A}{2} ##
Here I take t = 0.2s


Then, $$\omega t=0.2 \omega=\frac{2\pi}{3}\implies \frac{k}{0.9}=\frac{4\pi^2}{0.6^2}$$
Now this gives the correct answer.

This could either be a coincidence or even my initial interpretation is correct if period of motion in the question refers to time taken before first collision. [(-A) to (+A/2)]Could this question have two meanings? (POST 28)
 
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  • #32
Aurelius120 said:
before first collision. [(-A) to (+A/2)]
For the third time, it is not [(-A) to (+A/2)].
"Spring compressed to √2cm. "
A = √2cm.
"Block at 1/√2cm from wall."
Block starts at A/2 from wall; equilibrium is A from starting position, so A/2 to the right of the wall. The motion is an oscillation between -A and -A/2.
 
Last edited:

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