# Instantaneous response of damped simple harmonic motion

1. Apr 27, 2014

### james6008

Hi

I am trying to model SHM in Simulink as shown here:

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?

2. Apr 27, 2014

### 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.

3. Apr 27, 2014

### 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.

4. Apr 27, 2014

### 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.