Mass on a Spring: Solving for k and T with 100g and 1kg

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The discussion revolves around calculating the spring constant (k) and the period (T) for a steel spring under different weights. When a 100g weight is applied, the spring extends by 10cm, leading to a calculated spring constant of 9.81 N/m. However, when a 1kg weight is used, the spring constant is incorrectly recalculated as 98.1 N/m, which is not accurate since the spring constant remains the same for the same spring. The period of oscillation is also recalculated, but the misunderstanding lies in assuming the spring extends the same amount with different weights. The key takeaway is that the spring constant does not change, and the extension will differ with varying weights.
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Homework Statement


a steel spring that it extends by 10cm in equilibrium when you attach the upper end of the spring to a fixed support and hang a weight of 100g at the lower end.

And I found k and T, so how about if I change the weight to 1kg at the lower end and do the same thing?


Homework Equations


F = -kx



The Attempt at a Solution


I found they actually same.
when 100g
mg=kx
k=9.81

T=2pi*sqrt(m/k) = 2*pi*sqrt(0.1/9.81) = ...

when 1kg
mg=kx
k = 98.1
T=2pi*sqrt(m/k) = 2*pi*sqrt(1/98.1) = ...

same!?

I think I did wrong, who can help me?
THANK YOU!
 
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Why do you think the spring constant changes? If you are using the same spring, then you'll have the same spring constant. (You cannot assume that the spring extends by the same amount with a heavier weight hanging from it. If you do, then of course you'll get the same answer since m/k will be the same.)
 

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