Plasticine dropped on a block - Oscillation

[herich]

A plate of mass m is supported by a light spring fixed vertically on the ground. A plasticine is dropped gently onto the block when it is are the highest position. Which of the following statements is/are correct?
1) The amplitude of the oscillation would increase since the equilibrium position is lowed. (correct)
2) The amplitude of the oscillation would also increase if the plasticine is dropped gently onto the block when it is at the lowest position.
(incorrect)

I don't know why.

I also compare the question with the one that is similar:
For a mass-spring system resting on a smooth horizontal surface, amplitude decreases if a plasticine is dropped onto the mass when it is at the equilibrium position.

When should I consider the equilibrium position and when should I consider the total mass?

Thanks a lot.

 

[tiny-tim]

A plate of mass m is supported by a light spring fixed vertically on the ground. A plasticine is dropped gently onto the block when it is are the highest position. Which of the following statements is/are correct?
1) The amplitude of the oscillation would increase since the equilibrium position is lowed. (correct)
2) The amplitude of the oscillation would also increase if the plasticine is dropped gently onto the block when it is at the lowest position.
(incorrect)

I don't know why.

Hi herich!

Draw a nice big diagram and mark the highest and lowesst positions H and L, and the original and lowerd equilibirum positions E1 and E2.

What do you notice about them?

For a mass-spring system resting on a smooth horizontal surface, amplitude decreases if a plasticine is dropped onto the mass when it is at the equilibrium position.

Hint: consider the spring constant.

 

[herich]

Actually, I have the diagram already~
But I don't understand why at the highest position, the equilibrium will be lowered, but not when at the lowest position. Also, how about when the mass is at the original equilibrium position?
k=4*pi*pi*m/(T*T), m is changed, and T is not?
confused... =.=

 

[tiny-tim]

But I don't understand why at the highest position, the equilibrium will be lowered, but not when at the lowest position.

oh I see … you're misunderstanding the answer …

the equilibrium is lowered, when the plasticine is added at the lowest position …

it's the amplitude increasing that's wrong!

 

[herich]

I understand now! But what about when the plasticine is placed on the mass when the mass is in the original equilibrium position? The equilibrium will lower, right? (I think it is because the mass of the system increases)

But what about the horizontal system? When the mass increases, period also increase, and the angular velocity and amplitude decreases, if the plasticine is placed on the mass when the mass is in the original equilibrium position? How about the plasticine is placed at the extreme point?

 

[tiny-tim]

But what about the horizontal system?

Hint: Assuming the plasticine is dropped vertically, what immediately happens to the momentum and the speed?

 

[herich]

amplitude must decreases
And at the extreme point, amplitude will not change? (because at that point, the speed is 0)

And the last question, back to the condition when the plasticine is placed on the mass when the mass is in the original equilibrium position(vertical spring-mass). The equilibrium will lower, does the amplitude then increase?

 

[tiny-tim]

I'm sorry … you've lost me … we don't seem to be answering the same questions …

You had 1) and 2), which were vertical springs, with the plasticine added at top and bottom,

and the only other question was about a horizontal spring on a horizontal table, so that the added plasiticine does not change the equilibrium position.

 

[Topher925]

I am having difficulty following you as well. Like Tim stated, the problem is basically asking what's the difference between adding mass at the top and at the bottom of the springs positions. For 1) the amplitude will increase and 2) the amplitude will decrease like you stated.

And the last question, back to the condition when the plasticine is placed on the mass when the mass is in the original equilibrium position(vertical spring-mass). The equilibrium will lower, does the amplitude then increase?

When adding the plasticine at the equilibrium point, the amplitude will still increase. I like to take the energy approach to these kinds of problems. Think of the oscillating spring and mass an energy storage device. If the plasticine is not added at the lowest point of the spring oscillation, what will this do to the overall energy contained in the oscillating system?

 

[herich]

Sorry, "the last question" is the extra question I want to ask for clarifying my concept. So, I've concluded the above discussion as the following:

For vertical system:
- added at top, equilibrium position lowers and amplitude increases
- added at equilibrium position, equilibrium position lowers and amplitude increases
- added at bottom, equilibrium position lowers and amplitude decreasesFor horizontal system:
- added at extremes, amplitude is unchanged
- added at equilibrium position, amplitude decreases

And I now understand them now. Thanks~