Answer to Question #77770 in Classical Mechanics for Charvi

Question

If we apply 10 N force on a spring of spring constant 10 N/m and extend it by 0.1 m then how it will apply 10N force as a reaction force or restoring force against our action force to follow newtons 3rd law
And how will we know that applying a particular force will produce how much displacement
Would that be done by F=ma because F=kx is for knowing the restoring force

Answer 1

It's more Hooke's law that will fail. If you contrive to suddenly apply exactly 100 N to the spring then the spring will surely apply exactly 100 N to you, at the same moment. It's just that it won't be 100 N from an even compression of the normal working length of the spring, because, ex hypothesis, most of the spring hasn't had time to move. Rather, to begin with it, will be some tiny section near the tip, which being effectively shorter can be stiffer. And a wave of compression will travel along the spring until it's all compressed and then there will be overshoot and much bouncing around until everything finally settles down to the situation that Hooke's law is about.