Question

why do we wait for sometime after adding and removing of weight to the spring?

Answer 1

When, we remove a weight that was earlier suspended by the spring, the force in the spring does not instantly become zero because it takes the spring a finite time to reach to it's natural length and thus instantly adding another weights can cause personal errors in the experiment.

Answer 2

$\huge\blue{hey mate!!}$

We would not hey the equillibrium after an object is placed over it. So to get the equillibrium it is left undisturbed.

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