# External driving force on blackbox system: frequency response

• rookie4002
In summary, the conversation discusses the concept of external driving forces on a blackbox system, specifically the Earth being driven by the Sun. The question is raised if the response of the Earth to this force can have a period different from the driving force, and it is noted that this is possible in certain situations, such as with the emission of light from a laser every 3.8557 years. The limitations of studying a blackbox system and the potential for different responses, such as higher harmonics, are also mentioned.

#### rookie4002

External driving force on "blackbox" system: frequency response

Easy question:

I have a blackbox system (it's actually the Earth, but we can just treat it as a blackbox) driven externally by a periodic sinusoidal force (the Sun). If the driving force has a period of say 10 years, is there any way that the response of the Earth due to that force have anything but a period of 10 years once steady state has been reached? (which I think we can safely assume for the Earth-Sun system).

The answer seems intuitive enough, and obviously can be proved easily for pendulums and a lot of idealized systems, but I'm not 100% positive that it's always the case for ALL systems. Ideally there would be a math theorem or some physics proof perhaps, assuming a generic Lagrangian, that can prove that the response will also be sinusoidal with the same freq as the the driving frequency. Otherwise a counterexample would work just fine the other way.

Thanks for the help

Let humans shoot a laser in space every 3.8557 years. The emission of light of this wavelength clearly has a frequency different from 10 years.
It is a blackbox - you cannot look at causal connections inside. And maybe the 10-year-cycle of Earth inspired humans to build and use their lasers?

In terms of less intelligent setups: You can get different responses. The easiest things are higher harmonics from nonlinear reactions, but other frequencies can occur somehow, too.

## 1. What is an external driving force on a blackbox system?

An external driving force on a blackbox system refers to any input or signal that is applied to the system from an outside source. This could include physical forces, such as vibrations or pressure, or electrical signals, such as currents or voltages.

## 2. How does an external driving force affect the frequency response of a blackbox system?

The external driving force can greatly impact the frequency response of a blackbox system. The system's response to different frequencies will depend on the characteristics of the driving force and how it interacts with the system's components.

## 3. What is the frequency response of a blackbox system?

The frequency response of a blackbox system is a measure of how the system responds to different frequencies of an external driving force. It describes the system's ability to transmit or block certain frequencies and can be represented by a graph or equation.

## 4. How can the frequency response of a blackbox system be measured?

The frequency response of a blackbox system can be measured by applying a range of known input frequencies and measuring the corresponding output of the system. This data can then be used to create a frequency response plot or calculate the system's transfer function.

## 5. What factors can affect the frequency response of a blackbox system?

Several factors can influence the frequency response of a blackbox system, including the system's components, the characteristics of the external driving force, and any external disturbances. Changes in any of these factors can alter the system's response to different frequencies.