Instantaneous response of damped simple harmonic motion

[james6008]

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?

 

[AlephZero]

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.

 

[james6008]

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.

 

[AlephZero]

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.

 

[PJC01]

Hello,

It seems that you are trying to model a damped simple harmonic motion (SHM) system in Simulink. As you have noticed, the response of the system is dependent on the values of spring constant and damping. The damping factor plays a crucial role in determining the speed of response in a damped SHM system.

In your case, it seems that the damping factor of 15 is causing the system to respond with a delay of 1.5 seconds. This is because the higher the damping factor, the slower the system responds. To achieve a quicker response time of less than 0.5 seconds, you will need to decrease the damping factor. This can be done by either reducing the damping coefficient or increasing the spring constant.

Additionally, you can also try adjusting the mass and force values to see if that has an impact on the response time. It is important to note that the response time will also be affected by any external factors, such as friction or air resistance, which may not be included in your model.

I would also suggest exploring different methods of modeling SHM in Simulink, such as using different blocks or techniques, to see if that can improve the response time. Overall, the key is to find a balance between the spring constant and damping factor to achieve the desired response time. I hope this helps. Good luck with your modeling!