Understanding Damped Harmonic Motion Parameters: A Graphing Challenge

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In summary, the student is seeking confirmation on their calculations for the undamped natural frequency and damping ratio, as well as help with plotting a graph for question d. They also mention that their previous file was incorrect. The user suggests using the given equation to get the graph and questions the calculation for r. They are looking for an explanation for this calculation.
  • #1
matthew1982
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Homework Statement


Hi I have attemted to work out the undamped natural frequency and the damping ratio can someone please confirm if this is correct? and for question d I have worked out r and TR can someone please confirm if this is correct? if all is correct I need help with plotting a graph for question d with the parameters set at the bottom of the question can you please help me anyone?

Homework Equations

The Attempt at a Solution

 

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  • A dynamic mass.docx
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  • #2
Hi this is the correct file by the way the file on my first post is incorrect
 

Attachments

  • A dynamic mass.docx
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  • #3
In part D you are given the relationship between TR and r. You can use that equation to get the graph.
 
  • #4
Seeing $$r = {\omega\over \omega_n} = r = {10\over 22.4} = 3.565 $$ hurts my eyes (in more than one way). Can you explain this ?
 

1. What is dynamic mass/spring/damper?

Dynamic mass/spring/damper is a mechanical system that models the behavior of a mass attached to a spring and a damper. It is used to study the motion of objects in response to external forces.

2. How does dynamic mass/spring/damper work?

The system works by applying Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the mass from its equilibrium position. The damper in the system helps to dissipate energy and reduce the amplitude of the oscillations.

3. What are the applications of dynamic mass/spring/damper?

Dynamic mass/spring/damper systems are commonly used in engineering and physics to study the behavior of mechanical systems, such as car suspensions, buildings during earthquakes, and vibrating structures. They are also used in the design of shock absorbers and vibration isolators.

4. How is the behavior of the system affected by changes in the parameters?

The behavior of the system is affected by changes in the mass, spring stiffness, and damping coefficient. Increasing the mass or the stiffness of the spring will result in a slower response and larger amplitude of oscillations. On the other hand, increasing the damping coefficient will result in a faster response and smaller amplitude of oscillations.

5. Is there a real-life example of a dynamic mass/spring/damper system?

Yes, a car suspension system is an example of a dynamic mass/spring/damper system. The mass of the car is attached to the springs and dampers, which help to absorb the impact of bumps on the road and provide a smoother ride for the passengers.

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