Work done by force acting on a spring

[Studiot]

The objective is an energy balance or accounting.

(It's not a trick 'onest guv)

I'm merely observing that we can (I think) say that the mass has potential energy due to the elastic energy stored in the spring and thereofe the pull exerted by the spring.

This is eventually transferred to the mass as kinetic energy when it oscillates and forms the energy of the oscillation ie that which is transferred back and fore between KE and PE.

I want to end up by observing that the force F does work on the mass, which in turn does work on the spring when pulled out so the net energy of the mass does not increase when it has reached a stop at the maximum s₁

 

[Doc Al]

The objective is an energy balance or accounting.

(It's not a trick 'onest guv)

I'm merely observing that we can (I think) say that the mass has potential energy due to the elastic energy stored in the spring and thereofe the pull exerted by the spring.

This is eventually transferred to the mass as kinetic energy when it oscillates and forms the energy of the oscillation ie that which is transferred back and fore between KE and PE.

I want to end up by observing that the force F does work on the mass, which in turn does work on the spring when pulled out so the net energy of the mass does not increase when it has reached a stop at the maximum s₁

I prefer to say that the system (really the spring) has potential energy, not just the mass. (For the same reason I think it is misleading to talk about the gravitational PE of a mass--it's really the PE of the mass-earth system.)

The force F does work on the system. The mass essentially transmits the force to the spring, which gets spring PE as it is stretched. When the mass is allowed to oscillate, the spring and mass exchange energy.

I don't see the issue. (Or how it relates to the OP's concern.)

 

[Studiot]

it's really the PE of the mass-earth system.)

Yes that's true enough.
Thanks for your patience.