Exploring Matlab Step, Impulse, and Bode Functions in Physical Systems

[Jones1987]

So I understand what these inputs are, however I'm having a hard time visualising what they do in a physical system.

Can anyone share any physical examples of what each of these do?
E.G I assume a step input in a Mass Spring Damper system would create the force to cause oscillation?

 

[AlephZero]

Impulse = hit the system with a hammer, then let it do whatever it does.

Step = suddenly apply a constant force to the system, then keep the applying the force "for ever".

They will both produce oscillations transient in a spring-mass-damper system. For an impulse, the system will come back to the original position after hte oscillations die out. For a step, the system will end up with the spring extended by the constant force.

Steps and impulses can also be used as the building blocks to model other forces applied to a system. For example a step of +F at time 0, plus a step of -F at time 1, is the same applying the force for an interval of 1 second.

A bode plot is a way to displaying the response of the system to an oscillating force at different frequencies - for example to show what happens close to the resonant frequencies of the system.

 

[Jones1987]

Impulse = hit the system with a hammer, then let it do whatever it does.

Step = suddenly apply a constant force to the system, then keep the applying the force "for ever".

They will both produce oscillations transient in a spring-mass-damper system. For an impulse, the system will come back to the original position after hte oscillations die out. For a step, the system will end up with the spring extended by the constant force.

Steps and impulses can also be used as the building blocks to model other forces applied to a system. For example a step of +F at time 0, plus a step of -F at time 1, is the same applying the force for an interval of 1 second.

A bode plot is a way to displaying the response of the system to an oscillating force at different frequencies - for example to show what happens close to the resonant frequencies of the system.

Brilliant post, if I could rep you somehow I would!

This is exactly what I wanted to know. Really appreciate it, modelling systems will be so much easier now.

 

[rcfan]

I have a some difficulty in imagining how the step force input to the mass spring damper system could be given.

For example imagine a mass is suspended from the ceiling with the spring and damper between the mass and the ceiling - how would one give a step Force input to the system?

I thought that we could attach a weight to the existing mass that would exert a downward pull on the mass (i.e a constant force) - however the mass property of the original system would be altered and we would end up with a new system.

Also we could use a jack to apply the force on the mass but the jack would constrain the movement of the mass and the dynamics of the system would be altered.

So how does one apply a constant force to the mass - could you help me out ?

Many Thanks

 

[alphy]

Sure, let me provide some physical examples for each of the functions you mentioned.

1. Step Function: In a physical system, a step function represents a sudden change in a parameter or input. For example, in a heating system, turning on the heater would result in a step function as it suddenly increases the temperature. In a mechanical system, a step function could represent a sudden change in force or displacement.

2. Impulse Function: An impulse function represents a sudden, short-lived burst of energy in a physical system. For example, in a collision between two objects, the impact of the collision can be represented by an impulse function. In an electrical circuit, a sudden surge of current can also be represented by an impulse function.

3. Bode Function: The Bode function is used to analyze the frequency response of a physical system. It is commonly used in control systems to understand how a system responds to different input frequencies. For example, in a speaker system, the Bode function can be used to analyze how the system responds to different audio frequencies.

In summary, these functions are useful in understanding and analyzing physical systems, such as mechanical, electrical, and thermal systems. They can help us predict and design the behavior of these systems under different inputs and conditions. I hope this helps in visualizing their role in physical systems.