Oscillation with constrained amplitude

[VicomteDeLaFere]

TL;DR

Natural frequency oscillation when constrained: spring mass system on a table restraining amplitude

Hello,

Suppose we have a simple oscillating spring mass system. The natural frequency will excite the system to have infinite amplitude. Suppose then, that we have that system on a table so that amplitude is limited. I'm imagining the high school experiment with the spring mass system on the teacher's table. The teachers always stop before the mass hits the table.

What would the response look like if the table were higher and the oscillation amplitude of the mass was constrained to a certain distance? What if that constrained distance was the resting distance? That is to say, what if the mass naturally, barely rests on the table and there is a driving force at the natural frequency? Would the mass even begin moving?

Thank you (I need to buy a physics kit.)

 

[Orodruin]

The natural frequency will excite the system to have infinite amplitude.

This is only true in the idealised case where there are no dissipative forces involved. In a more realistic scenario, amplitude is constrained by the energy loss over one period being equal to the energy put into the system by the driving force.

What would the response look like if the table were higher and the oscillation amplitude of the mass was constrained to a certain distance? What if that constrained distance was the resting distance? That is to say, what if the mass naturally, barely rests on the table and there is a driving force at the natural frequency? Would the mass even begin moving?

It is difficult to tell exactly what you are imagining. If you restrain the amplitude by an external force, your system will no longer be describable in terms of a driven harmonic oscillator.

 

[sophiecentaur]

(I need to buy a physics kit.)

No real need for this. Most of these problems can be solved in your head, although a Physics Kit can be fun.

amplitude of the mass was constrained to a certain distance

So the mass bumps against the floor? Then it could lose all its Kinetic energy and there would only be one cycles worth of Energy in the system and there would be no build up of energy. If there is an elastic collision with the floor (some bounce), then the mass would rise at a time that the exciting force is not occurring at the right time. The situation is then much more complicated, as @Orodruin says and the simple harmonic oscillator analysis no longer applies. Depending on the details of timing and distances, you could get some energy build up in the system with a very complicated form of motion.
These scenarios are a year or more down the road from SHM in your studies.