How Quickly Does a Spring's Restoring Force Counteract Applied Force?

[chandran]

Let me start with Newton second law,a mass m acted upon by force f will accelerate to f/m

Let me consider a spring fixed to one end and a mass(call m1) attached to other end.

when i apply a force f to the mass(m1) it shouldl accelerate to a=f/m1 if Newtons law is to be obeyed.

But since the spring has a restoring force the mass doesn't accelerate. But at what time the restoring force comes into picture. Will the spring take some time before it applies a restoring force=applied force. If it takes some time to apply restoring force in that duration the force f must have given the mass m a much higher acceleration and ..... the mass will accelerate. I need some discussion on this ...

 

[Homer Simpson]

The force you are talking about is not directly applied to the mass, its applied to the spring. The spring will compress to some degree as the force is applied, all depending on how big of a force and how quickly it is applied. The reason the mass could wind up having a higher accelleration is because the force was applied for some length of time into the spring. The spring compresses, potential energy. In the end the conservation of energy and momentum will be shown.

 

[Doc Al]

when i apply a force f to the mass(m1) it shouldl accelerate to a=f/m1 if Newtons law is to be obeyed.

Realize that it is the net force on the mass that determines the acceleration; the net force will be the combination of applied force and the spring's restoring force. The restoring force acts whenever the mass is displaced from equilibrium.