Maximizing Mass Motion with Minimal Hand Movement

In summary, a student is able to create an oscillating motion in a 3 kg mass attached to a real spring with a spring constant of 94 N/m and a damping constant of 0.6 N sec/m. To achieve maximum motion of the mass with minimum motion of her hand, the student should move her hand at an approximate frequency of 0.890886 seconds. When the student stops moving her hand, it will take some time for the mass to come to rest and reach half of its maximum amplitude, but the equation of motion is needed to determine the exact time.
  • #1
wolves5
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A student gets a 3 kg mass to oscillate up and down on bottom of a light vertical spring by pulling her hand up and down on the top end of the spring. The spring is a real spring with a spring constant of 94 N/m and a damping constant of 0.6 N sec/m.

(a) At what approximate frequency should the student move her hand up and down to get the maximum motion from the mass with the minimum motion of her hand?

The frequency I got was 0.890886 and its correct. I did 2pi times (sq.rt 3/94) and got 1.12247. To get frequency, I did 1/1.12247 and got 0.890886 seconds.

(b) The student now stops moving her hand and the mass slowly comes to rest. How long after she stop shaking her hand will it take for the amplitude of the mass to reach one half its maximum amplitude?

I don't know how to start this.
 
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  • #2
Do you know the equation of motion for the mass? If not, I'm pretty sure your physics textbook solves for it somewhere, so try looking for that.
 

FAQ: Maximizing Mass Motion with Minimal Hand Movement

1. What is "Maximizing Mass Motion with Minimal Hand Movement"?

"Maximizing Mass Motion with Minimal Hand Movement" is a theory that focuses on optimizing the amount of mass that can be moved with minimal hand movement. This theory is often applied in fields such as engineering, physics, and biomechanics.

2. How does this theory apply to everyday life?

One example of how this theory can be applied in everyday life is in the design of tools and equipment. By maximizing mass motion with minimal hand movement, tools and equipment can be designed to be more efficient and ergonomic for users.

3. What are the benefits of using this theory?

The benefits of using this theory include increased efficiency, reduced physical strain and fatigue, and improved performance. It can also lead to cost savings in industries where heavy machinery is used.

4. Are there any limitations to this theory?

One limitation of this theory is that it may not always be possible to maximize mass motion with minimal hand movement, especially in situations where there are safety concerns or other constraints. Additionally, this theory may not apply to all types of tasks or movements.

5. How can this theory be further researched and developed?

Further research can be conducted to explore the potential applications of this theory in various industries and fields. This can also involve developing new technologies and techniques for optimizing mass motion with minimal hand movement.

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