Instantaneous response of damped simple harmonic motion

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Discussion Overview

The discussion centers around modeling damped simple harmonic motion (SHM) in Simulink, specifically addressing the response time of the model to input forces. Participants explore the relationship between mass, spring constant, damping, and the frequency of the system's response, with a focus on achieving a quicker response time.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant describes their attempt to model SHM and notes a delay in response time that is influenced by damping and spring constant values.
  • Another participant suggests that the frequency of the response in SHM is dependent on mass and stiffness, proposing to test the model with lower damping values to observe changes in response.
  • A participant provides the formula for angular frequency and calculates the required spring constant to achieve a frequency greater than 2 Hz, indicating that a spring constant of 790 is necessary for a response time of < 0.5 seconds, which they consider impractically high.
  • Concerns are raised about the system's stability when the spring constant is increased too much, leading to an unstable response.
  • Another participant challenges the initial claim about the flexibility of the spring constant, suggesting that to achieve a faster response, the spring constant must be significantly increased, while also questioning the simulation's accuracy if it leads to infinite responses.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of achieving a faster response time through adjustments to the spring constant and damping. There is no consensus on the optimal values or the underlying issues affecting the model's stability.

Contextual Notes

Participants reference specific values for mass, force, spring constant, and damping, but there are unresolved questions regarding the limits of these parameters and their impact on system behavior. The discussion also highlights potential issues with the simulation setup that may not be fully addressed.

james6008
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Hi

I am trying to model SHM in Simulink as shown here:
http://pundit.pratt.duke.edu/wiki/Simulink/Tutorials/DiffEq

I have tried using different values of spring constant and damping to get instant response to the input force. I am measuring the displacement calculated by SHM. The force changes with time and the model responds to the change but the response is delayed by a certain amount of time which depends on damping mostly but sometimes its due to spring constant too. I can not get the model to respond any quicker than 1.5 seconds. I would like it to respond in < 0.5s. I have mass of 5kg, force about 30N/m, spring constant of 35 and damping of 15. I am allowed to change the spring constant and damping as I like.

Any idea what could be causing the problem?
 
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Do you know how the frequency of the response in SHM depends on the mass and stiffness?

If you don't know the "formula", try setting the damping to a small value like 1 and see what happens with different spring constants.

If you do know the formula, work out what spring constant you need to get the frequency high enough. If you want a response in < 0.5 sec the frequency needs to be > 2 Hz.
 
Hi

I believe the formula you are talking about is:

w = sqrt (k / m )

m = 5kg and I can re-arrange this to calculate the spring constant (k) for 2 Hz. I get a value of 790 which is way too high. In order to get a response of 1.5s I am using k=45.

Another problem with the model is that if you increase the spring constant too much, the system never stabilises and the response starts going in the opposite direction infinitely.
 
In your OP you said you could have any spring constant you like. Now you changed the rules and said 790 is too high!

If you are getting the response you want in 1.5 sec, but you want to speed it up to 0.5 sec, that is multiplying the frequency by 3. So using the formula you need to multiply the stiffness by 32 = 9 which would give k = about 400.

If your response goes to infinity when k is high, there must be something else wrong with your simulation.
 

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