Simple Harmonic Motion mass homework

[Peter G.]

Hi,

I am not very good with questions that ask me to asses a scenario qualitatively in SHM... So, if you guys can maybe guide/advise me how to go about these here:

1.A body is suspended vertically at the end of a spring that is attached to the ceiling of an elevator. The elevator moves with constant acceleration. Discuss the effect, if any, on the acceleration of the mass when the acceleration is downwards and upwards.

I tried thinking in terms of the forces on the mass when the elevator is accelerating upwards: (tension in the spring must exceed the weight of the mass) and on the way down (weight must exceed tension in the spring) but I thought greater forces would increase the amplitude and that has no effect on the period but I am probably not correct. I don't know, I really need some help on this one!

2. Discuss qualitatively the effects of this, if any, on the amplitude and period of oscillation in the following two separate cases in which the putty lands on the block: a) When the block moves past its equilibrium position and b) when the block is momentarily at rest at maximum displacement

So, if the putty lands on the mass, the mass of the system will increase, hence, the acceleration will decrease in both cases. When the acceleration decreases the amplitude or the omega has to change... I don't know...

I hope this is enough evidence I've been extracting as much of my brain as possible!

Thanks,
Peter G.

 

[PeterO]

Hi,

I am not very good with questions that ask me to asses a scenario qualitatively in SHM... So, if you guys can maybe guide/advise me how to go about these here:

1.A body is suspended vertically at the end of a spring that is attached to the ceiling of an elevator. The elevator moves with constant acceleration. Discuss the effect, if any, on the acceleration of the mass when the acceleration is downwards and upwards.

I tried thinking in terms of the forces on the mass when the elevator is accelerating upwards: (tension in the spring must exceed the weight of the mass) and on the way down (weight must exceed tension in the spring) but I thought greater forces would increase the amplitude and that has no effect on the period but I am probably not correct. I don't know, I really need some help on this one!

2. Discuss qualitatively the effects of this, if any, on the amplitude and period of oscillation in the following two separate cases in which the putty lands on the block: a) When the block moves past its equilibrium position and b) when the block is momentarily at rest at maximum displacement

So, if the putty lands on the mass, the mass of the system will increase, hence, the acceleration will decrease in both cases. When the acceleration decreases the amplitude or the omega has to change... I don't know...

I hope this is enough evidence I've been extracting as much of my brain as possible!

Thanks,
Peter G.

One way is to look at this is as "fictitious forces in an accelerated frame of reference".

If the mass was hanging on the spring in a stationary lift, the spring would be extended a certain amount - the distance determined by the mass and the spring constant. Now the mass does not alter during these observations.

If the lift is accelerating up, the spring will be stretched a little more. From the "ficticious force" idea, this means the spring is behaving as if it has a smaller spring constant [the spring is weaker]. This "new spring constant will result in a different period of oscillation.

If the lift is accelerating down, the spring will be extended less than before. The spring will be behaving as if it is stronger - has a higher spring constant. This will have an affect on the period of oscillation as well.