Graphs of s, v and a for a mass with a piece of paper attached

In summary, a mass with a piece of paper attached to it will have a displacement graph that looks like a sine wave, and the energy-time graph will look like a ramp.
  • #1
AN630078
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Homework Statement
Hello, I am really struggling to sketch the following graphs to show how a mass with a piece of paper attached to it varies with time, over a time period of 2T, for: 1. Energy 2. Displacement 3. Velocity 4. Acceleration
Relevant Equations
x=Acosωt v=-ωAsinωt a=-ω^2Acosωt
I understand that velocity is defined as the rate of change of position or the rate of displacement; and that acceleration is defined as the rate of change of velocity (it is the derivative of velocity).
Morever, I believe I know that for SHM these graphs vary sinusoidally (I have attached a picture of how I think these should appear).
However, for a mass with a piece of paper attached could these graphs be represented by a harmonic oscillator with a small amount of damping? I really do not know where to begin in drawing these, I am very confused.
 

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  • Screenshot 2021-04-13 at 19.40.02.png
    Screenshot 2021-04-13 at 19.40.02.png
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  • #2
It's not clear what is the significance of the piece of paper! Is this a translation?
 
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  • #3
PeroK said:
It's not clear what is the significance of the piece of paper! Is this a translation?
I have no idea, I really am very confused. The question just states " Sketch the following graphs to show how a mass with a piece of paper attached to it varies with time, over a time period of 2T"
 
  • #4
So, the net force is no longer a constant...
you need to model the new net force... a constant plus a new contribution.

If it were damped, what would a sketch of the position-vs-time graph look like?
From that get the other two
[velocity-vs-time is a graph of the slopes of the position-vs-time graph,
acceleration-vs-time is a graph of the slopes of the velocity-vs-time graph
https://phet.colorado.edu/en/simulation/legacy/calculus-grapher [uses Flash]
Not quite as arbitrary as above (but more constructive]:
https://www.geogebra.org/m/dzxdbzAR
https://www.geogebra.org/m/ezKv36tC
]
Or one could work from the acceleration-vs-time [since you know the net force], then get the other two.

Possibly helpful.
https://www.wired.com/2017/04/lets-study-air-resistance-coffee-filters/
 
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  • #5
robphy said:
So, the net force is no longer a constant...
you need to model the new net force... a constant plus a new contribution.

If it were damped, what would a sketch of the position-vs-time graph look like?
From that get the other two
[velocity-vs-time is a graph of the slopes of the position-vs-time graph,
acceleration-vs-time is a graph of the slopes of the velocity-vs-time graph
https://phet.colorado.edu/en/simulation/legacy/calculus-grapher [uses Flash]
Not quite as arbitrary as above (but more constructive]:
https://www.geogebra.org/m/dzxdbzAR
https://www.geogebra.org/m/ezKv36tC
]
Or one could work from the acceleration-vs-time [since you know the net force], then get the other two.

Possibly helpful.
https://www.wired.com/2017/04/lets-study-air-resistance-coffee-filters/
Thank you for your reply. I have attached what I think the displacement tie graph for a draped oscillator would look like. However, I am uncertain how to find the v-t and a-t graphs from this? Would this be correct anyhow for the s-t graph?
 

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  • Screenshot 2021-04-13 at 21.52.11.png
    Screenshot 2021-04-13 at 21.52.11.png
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  • #6
And would the energy-time graph for a damped oscillator be as shown in the attachment ?
 

Attachments

  • Screenshot 2021-04-13 at 21.55.52.png
    Screenshot 2021-04-13 at 21.55.52.png
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Related to Graphs of s, v and a for a mass with a piece of paper attached

1. What is the purpose of graphing s, v, and a for a mass with a piece of paper attached?

The purpose of graphing s, v, and a for a mass with a piece of paper attached is to visually represent the position, velocity, and acceleration of the mass as it moves with the paper attached. This can help in understanding the relationship between these variables and how they change over time.

2. How is the position (s) of the mass with the paper attached related to time?

The position (s) of the mass with the paper attached is related to time by the slope of the position-time graph. The steeper the slope, the greater the velocity of the mass. The position can also be calculated by finding the area under the velocity-time graph.

3. What does the velocity (v) of the mass with the paper attached indicate?

The velocity (v) of the mass with the paper attached indicates the rate of change of the position (s) over time. A positive velocity indicates that the mass is moving in the positive direction, while a negative velocity indicates movement in the negative direction. The slope of the velocity-time graph represents the acceleration of the mass.

4. How is the acceleration (a) of the mass with the paper attached calculated?

The acceleration (a) of the mass with the paper attached is calculated by finding the slope of the velocity-time graph. This represents the rate of change of velocity over time. A positive slope indicates a positive acceleration, while a negative slope indicates a negative acceleration.

5. Can the graphs of s, v, and a for a mass with a piece of paper attached be used to predict future motion?

Yes, the graphs of s, v, and a for a mass with a piece of paper attached can be used to predict future motion. By analyzing the trends and patterns in the graphs, one can make predictions about the future position, velocity, and acceleration of the mass. However, external factors such as friction and air resistance may also affect the motion of the mass.

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